Answer:
Interquartile range IQR = 5.5
Step-by-step explanation:
Interquartile range IQR = third quartile Q3 - first quartile Q1
IQR = Q3 - Q1 ........1
arranging the data in ascending order;
1,3,5,6,6,7,8,11,12
The median of the data is the 5th number which is 6
Separating the data into two halves;
(1,3,5,6,),6,(7,8,11,12)
The first quartile Q1 is; (the median of the first half)
Q1 = (3+5)/2 = 4
The third quartile Q3 is; (the median of the second half)
Q3 = (8+11)/2 = 9.5
The interquartile range IQR can be derived using equation 1;
IQR = Q3 - Q1 = 9.5 - 4
IQR = 5.5
Ben's employer will reimburse him $0.13 per mile driven. If Ben drives 210.1 miles on a business trip, what is his mileage reimbursement?
Answer:
27.31
Step-by-step explanation:
Take the number of miles and multiply by the reimbursement rate
210.1 * .13
27.313
Round to the nearest cent
27.31
You spin a spinner that has 15 equal-sized sections numbered 1 to 15. Find the theoretical probability of: P(odd number)
Answer: The correct answer is
Step-by-step explanation:
The probability of P(odd number) for odd numbers is 8/15
What is probability?Probability is a branch of mathematics that deals with the occurrence of a random event. For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.
According to question
A spinner that has 15 equal-sized sections numbered 1 to 15.
Total number of selection = 15
therefore odd no's are = 1,3,5,7,9,11,13,15 in total 8
And even no's are = 2,4,6,8,10,12,14 in total 7
Now probability of: P(odd number) = [tex]\frac{Total odd no's }{Total number of selection}[/tex]
= 8/15
Hence, the probability of odd number is 8/15
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$1,034,473.45 spell it out
Answer:
One million, thirty four thousand, four hundred and seventy three dollars and forty five cents.
What is the mean of the following set of data?
{4,3,1, 6, 1,7}
Answer:
3.6666666.... and continuing
or 3.7 if you want to round
Step-by-step explanation:
To find the mean, I added all the numbers up:
4+3+1+ 6+ 1+7 = 22
Then I divided that by how many numbers there are total (6).
22/6= 3.66666.. or 3.6 with a bar symbol on top of the 6.
Thus, the answer is 3.666666...
If a number ends in zero, then it is divisible by five
Answer:
Yes
Step-by-step explanation:
10,20,30,40,50 are all divisible by 5.
what is the value of x in the equation 4x +8y, when y =0.8?
Answer:
-1.6
Step-by-step explanation:
4x +8y=0
y=0.8 ⇒
4x+8*0.8=04x+6.4=04x=-6.4x= -6.4/4x= -1.6at noon a train leaves Washington DC headed for Charleston South Carolina a distance of 500 Miles the train traveling at a speed of 44 miles at 1 p.m. a second train leaves Charleston heading for Washington DC traveling 32 miles an hour how long after the train view Charleston where the trains pass each other
Insect Weights Consider a dataset giving the adult weight of species of insects. Most species of insects weigh less than 5 grams, but there are a few species that weigh a great deal, including the largest insect known: the rare and endangered Giant Weta from New Zealand, which can weigh as much as 71 grams. Is the shape of the distribution symmetric, skewed to the right, or skewed to the left
Answer:
Step-by-step explanation:
71 grams would definitely be an outlier on the high side, whereas "most" species would weigh much less. Thus, the graph of this distribution of weights would be skewed towards the lower side, that is, to the left.
The skewness of a dataset is a measure of deviation of a random variable from the normal distribution.
The shape of the distribution is skewed to the right
From the question, we understand that:
Most of the species are less than 5 grams.One specie weighs 71 grams71 is a very large dataset, compared to the other weight of the species.
This means that
71 is an outlier of the dataset.The dataset is concentrated at the left (less than 5)When there are much data at the left of a distribution, then the distribution is positively skewed.
Hence, the shape of the is skewed to the right
See attachment for illustration of skewness of a distribution.
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The function f determines the cost (in dollars) of a new Honda Accord in terms of the number of years t since 2000. That is, f ( t ) represents the cost (in dollars) of a new Honda Accord t years after 2000. Use function notation to represent each of the following. The cost (in dollars) of a new Accord in 2006?
A. How much more a new Accord costs in 2013 as compared to the cost of a new Accord in 2010?
B. A new Accord in 2013 is how many times as expensive as a new Accord in 2010?
C. $980 dollars more than the cost of a new Accord in 2016.
Complete Question
The function f determines the cost (in dollars) of a new Honda Accord in terms of the number of years t since 2000. That is, f ( t ) represents the cost (in dollars) of a new Honda Accord t years after 2000. Use function notation to represent each of the following. The cost (in dollars) of a new Accord in 2006?
A. How much more a new Accord costs in 2013 as compared to the cost of a new Accord in 2010?
B. A new Accord in 2013 is how many times as expensive as a new Accord in 2010?
C. In 2016 , some cars cost $980 more than the cost of a new Accord.How much does the other cars cost (in dollars)in 2016?
Answer:
a
The cost of a new Accord in 2013 compared to 2010 is z = f(13) - f(10)
b
The magnitude at which the cost of a new Accord in 2013 is greater than the cost in 2010 is
[tex]x = \frac{f(13)}{f(10)}[/tex]
c
The cost of the other cars is 2016 is r = 980 + f(16)
Step-by-step explanation:
From the question we are told that
The cost (in dollars) of a new Honda Accord is f(t)
Where t is number of years after 2000
The cost of the Honda Accord at 2013 is
f(2013 - 2000) = f(13)
The cost of the Honda Accord at 2010 is
f(2010 - 2000) = f(10)
So the cost difference between 2013 and 2010 is mathematically evaluated as
z = f(13) - f(10)
Let constant at which the cost of Honda Accord in 2013 is greater than its cost at 2010 be x
So
f(13) = x f(10)
=> [tex]x = \frac{f(13)}{f(10)}[/tex]
The cost of the Honda Accord in 2016 is mathematically evaluated as
f(2016 - 2000) = f(16)
Now the cost of these other cars is mathematically evaluated as
r = 980 + f(16)
The difference between the cost of Accord in 2013 and 2010 is [z = f(13) - f(10)] and this can be determined by using the given data.
Given :
f(t) represents the cost (in dollars) of a new Honda Accord t years after 2000.
A). The cost of Accord in 2013 is given by:
[tex]f(2013-2000) = f(13)[/tex]
The cost of Accord in 2010 is given by:
[tex]f(2010-2000) = f(10)[/tex]
So, the difference between the cost of Accord in 2013 and 2010 is:
z = f(13) - f(10)
B). Let the constant be 'a' then the value of 'a' is:
[tex]a = \dfrac{f(13)}{f(10)}[/tex]
So, the new Accord in 2013 'a' times as expensive as a new Accord in 2010.
C). Cost of the Honda Accord in 2016 is:
[tex]f(2016-2000) = f(16)[/tex]
The cost of the other cars is:
r = 980 + f(16)
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la suma de la longitud de una semicircunferencia y su diametro es 4(pi+2)cm . determine el arrea del circulo
Answer: [tex]16\pi \;cm^2[/tex]
Step-by-step explanation:
La longitud de una semicircunferencia es [tex]l=\pi r[/tex]
[tex]\pi r+2r=4(\pi+2)\\r(\pi+2)=4(\pi+2)\\r = 4\frac{\pi+2}{\pi+2} \\r=4[/tex]
[tex]A = \pi r^2 = \pi (4)^2=16\pi[/tex]
Write an equation for "nine times a number decreased by five is the same as six times the same number increased by seven.
Answer: 9*x-5 = 6*x+7
Step-by-step explanation:
First we have to understand what it is saying.
9 times x (being a number) minus 5 equal to 6 times x plus 7
Now lets put it into an equation.
[tex]9*x-5 = 6*x+7[/tex]
Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations.
(a) The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. If required, round your answer to four decimal places.
(b) Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. If required, round your answer to four decimal places.
(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?
Answer:
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}[/tex] to four decimal places.
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}[/tex] to four decimal places.
Step-by-step explanation:
a)
Assuming X to be the random variable which replace the amount of defectives and follows standard normal distribution whose mean (μ) is 10 ounces and standard deviation (σ) is 0.15
The values of the random variable differ from mean by ± 1 \such that the values are either greater than (10+ 0.15) or less than (10-0.15)
= 10.15 or 9.85.
The probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:
[tex]P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.15}< \dfrac{X-10}{0.15}< \dfrac{10.15-10}{0.15})[/tex]
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- \phi (1) - \phi (-1)[/tex]
Using the Excel Formula ( = NORMDIST (1) ) to calculate for the value of z =1 and -1 ;we have: 0.841345 and 0.158655 respectively
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- (0.841345-0.158655)[/tex]
[tex]P(X < 9.85 \ or \ X> 10.15) =0.31731[/tex]
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}[/tex] to four decimal places.
b) Through process design improvements, the process standard deviation can be reduced to 0.05.
The probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:
[tex]P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.05}< \dfrac{X-10}{0.05}< \dfrac{10.15-10}{0.05})[/tex]
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- \phi (3) - \phi (-3)[/tex]
Using the Excel Formula ( = NORMDIST (3) ) to calculate for the value of z =3 and -3 ;we have: 0.99865 and 0.00135 respectively
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- (0.99865-0.00135)[/tex]
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}[/tex] to four decimal places.
(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?
The main advantage of reducing the process variation is that the chance of getting the defecting item will be reduced as we can see from the reduction which takes place from a to b from above.
Round 0.043118 to 1 significant figure.
Answer:0.04
Step-by-step explanation:numbers from 0-4 are rounded off while numbers from 5-9 are rounded up by adding 1 to the number before. Significant number are numbers from 1above
Therefore 0.043118 to 1 significant number is 0.04
The number 0.043118 rounded to 1 significant figure is given by the equation A = 0.04
What is rounding up numbers?There are basically two rules while rounding up numbers
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Non-zero digits are always significant
Zeros between non-zero digits are always significant
Leading zeros are never significant
Trailing zeros are only significant if the number contains a decimal point
Given data ,
Let the number be represented as n
The value of n = 0.043118
Let the rounded number be represented as A
So , when rounding the number to one significant number , the leading zeros are never significant and non-zero digits are always significant
Substituting the values in the equation , we get
A = 0.04
Hence , the rounded number is 0.04
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how many whole numbers are there between 40 and 75
Answer:
2
Step-by-step explanation:
50 and 60
Answer: 35 whole numbers.
Step-by-step explanation:
You could just find the difference between the numbers or list the numbers.
75-40=35
Or, 41,42,43,44,45,46,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74.
All these numbers are whole numbers between 40 and 75 and they all count up to 35.
You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands. (Hint: if an individual has no ability to distinguish between the two soft drinks, then each brand is equally likely to be selected.)(a) What is the probability that the sample will have between 50% and 60% of the identification correct?(b) The probability is 90% that the sample percentage contained within what symmetrical limits of the population percentage?(c) What is the probability that the sample percentage of correct identifications is greater than 65%?
Answer:
a) probability that the sample will have between 50% and 60% of the identification correct = 0.498
b) The probability is 90% that the sample percentage is contained 45.5% and 54.5% of the population percentage
c) Probability that the sample percentage of correct identifications is greater than 65% = 0.01
Step-by-step explanation:
Sample size, n = 200
Since the brands are equally likely, p = 0.5, q = 0.5
The Standard deviation, [tex]\sigma_p = \sqrt{\frac{pq}{n} }[/tex]
[tex]\sigma_p = \sqrt{\frac{0.5 * 0.5}{200} } \\\sigma_p = 0.0353[/tex]
a) probability that the sample will have between 50% and 60% of the identification correct.
[tex]P(0.5 < X < 0.6) = P(\frac{0.5 - 0.5}{0.0353} < Z < \frac{0.6 - 0.5}{0.0353} )\\P(0.5 < X < 0.6) = P( 0 < Z < 2.832)\\P(0.5 < X < 0.6) = P(Z < 2.832) - P(Z < 0)\\P(0.5 < X < 0.6) = 0.998 - 0.5\\P(0.5 < X < 0.6) = 0.498[/tex]
Probability that the sample will have between 50% and 60% of the identification correct is 0.498
b) p = 90% = 0.9
Getting the z value using excel:
z = (=NORMSINV(0.9) )
z = 1.281552 = 1.28 ( 2 dp)
Then we can calculate the symmetric limits of the population percentage as follows:
[tex]z = \frac{X - \mu}{\sigma_p}[/tex]
[tex]-1.28 = \frac{X_1 - 0.5}{0.0353} \\-1.28 * 0.0353 = X_1 - 0.5\\-0.045+ 0.5 = X_1\\X_1 = 0.455[/tex]
[tex]1.28 = \frac{X_2 - 0.5}{0.0353} \\1.28 * 0.0353 = X_2 - 0.5\\0.045+ 0.5 = X_2\\X_2 = 0.545[/tex]
The probability is 90% that the sample percentage is contained 45.5% and 54.5% of the population percentage
c) Probability that the sample percentage of correct identifications is greater than 65%
P(X>0.65) = 1 - P(X<0.65)
[tex]P(X<0.65) = P(Z< \frac{X - \mu}{\sigma} )\\P(X<0.65) = P(Z< \frac{0.65 - 0.5}{0.0353} )\\P(X<0.65) = P(Z < 4.2372) = 0.99\\P(X>0.65) = 1 - P(X<0.65)\\P(X>0.65) = 1 - 0.99\\P(X>0.65) = 0.01[/tex]
Which ordered pair is a solution of the equation?
y-3=5(x-2) Choose 1 answer:
A
Only (2,3)
B
Only (3,2)
C
Both (2,3) (3,2)
D
Neither
Answer:
A Only (2, 3)
Step-by-step explanation:
The given equation is in point-slope form:
y -k = m(x -h) . . . . . a line with slope m through point (h, k)
The point in the given equation is ...
(h, k) = (2, 3)
so you know the equation is satisfied at that point.
__
When you try the other point, you find ...
For (x, y) = (3, 2), you have
2 -3 = 5(3 -2)
-1 = 5(1) . . . . FALSE
Point (3, 2) does not satisfy the equation.
Only (2, 3) is a solution of the equation
_____
Of course, the equation of a line is satisfied by an infinite number of points. Of the two listed here, only (2, 3) is a solution.
A cube has sides that are 3 in. long. What is the surface area of the cube?
OA) 72 in2
OB) 54 in 2
OC) 36 in2
OD) 61 in 2
Answer:
B 54in
Step-by-step explanation:
Michael puts 21 sports cards into stacks of 3. The answer is 7. What’s the question?
There are 232 people waiting in line for
an amusement park ride. Each car on
the ride will be filled with 5 people.
How many cars are needed to hold all
the people waiting in line?
TRY IT
Answer:
232 ÷ 5 = 46.4
you will need 47 cars.
Some parts of California are particularly earthquake- prone. Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let X denote the number among the four who have earthquake insurance. a. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with proba bility (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes.] b. Draw the corresponding probability histogram. c. What is the most likely value for X
Answer:
a. Binomial random variable (n=4, p=0.25)
b. Attached.
c. X=1
Step-by-step explanation:
This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).
a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{4}{k} 0.25^{0}\cdot0.75^{4}[/tex]
The sample space for X is {0,1,2,3,4}
The associated probabilties are:
[tex]P(x=0) = \dbinom{4}{0} p^{0}(1-p)^{4}=1*1*0.3164=0.3164\\\\\\P(x=1) = \dbinom{4}{1} p^{1}(1-p)^{3}=4*0.25*0.4219=0.4219\\\\\\P(x=2) = \dbinom{4}{2} p^{2}(1-p)^{2}=6*0.0625*0.5625=0.2109\\\\\\P(x=3) = \dbinom{4}{3} p^{3}(1-p)^{1}=4*0.0156*0.75=0.0469\\\\\\P(x=4) = \dbinom{4}{4} p^{4}(1-p)^{0}=1*0.0039*1=0.0039\\\\\\[/tex]
b. The histogram is attached.
c. The most likely value for X is the expected value for X (E(X)).
Is calculated as:
[tex]E(X)=np=4\cdot0.25=1[/tex]
At a car rental agency, 0.39 of the cars are returned on time. A sample of 12 car rentals is studied. What is the probability that more than 3 of them are returned on time?
Answer:
Probabilty of more than 3 =0.8474
Step-by-step explanation:
Probabilty of returned on time P= 0.39
Probabilty of not on time q=1-0.39= 0.61
Sample = 12 cars
Selected items = 3 cars
Probabilty of3 returned on time
= 12C3 * (0.39)^3 * (0.61)^9
= 220*(0.059319)*(0.011694146)
= 0.1526
Note**** C represents combination
So probability of more than 3 means greater than 3 = from 4 above
Probability of more than 3 = 1-probability of three
Probabilty of more than 3 = 1-0.1526
Probabilty of more than 3 =0.8474
need help!!!! asap!!!!
Answer:
number 15 would be B sorry i dont understand number 14
Can someone please answer this quick!
It is recommended that one smoke detector be installed for every 500 square feet of floor area in a building. Write an equation to determine s, the number of smoke detectors needed for a building with 7,250 Square feet of floor space.
How many smoke detectors are needed for that building?
Answer:
Equation- 7,250 divided by 500
Answer- 15
Step-by-step explanation:
thanks google for letting me look this up! ;)
Answer:
s = 7,250/500
Step-by-step explanation:
If you want a smoke detector every 500 feet you divide the total amount (7,250) into (s) many 500 foot spaces. This means that you could also divide 7,250 by 500 ft to get s or the number of smoke detectors needed.
What is the inverse of the function G(X)=-2(x-4)
Answer:
Step-by-step explanation:
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The inverse of the function G(X)=-2(x-4) is G'(x) = -(1/2)x +4
What is a Function?A function is a law that relates a dependent and an independent variable.
The function is g(x) = -2(x-4)
The inverse of a function is found by interchanging the position of the x an d y variable and then solving for y in terms of x.
g(x) = -2 (x-4)
y = -2(x-4)
Interchanging y to x
x = -2( y-4)
x = -2y +8
(x - 8)/ -2 = y
y = 4 - (1/2)x
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Suppose that theta is an angle in standard position whose terminal side Intersects the unit circle at (-11/61, -60/61)
Find the exact values of tan theta, sec theta, and cos theta.
Answer:
The exact values of the tangent, secant and cosine of angle theta are, respectively:
[tex]\cos \theta = -\frac{11}{61}[/tex]
[tex]\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}[/tex]
[tex]\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}[/tex]
Step-by-step explanation:
The components of the unit vector are [tex]x = -\frac{11}{61}[/tex] and [tex]y = -\frac{60}{61}[/tex]. Since [tex]r = 1[/tex], then [tex]x = \cos \theta[/tex] and [tex]y = \sin \theta[/tex]. By Trigonometry, tangent and secant can be calculated by the following expressions:
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}[/tex]
[tex]\sec \theta = \frac{1}{\cos \theta} = \frac{1}{x}[/tex]
Now, the exact values of the tangent, secant and cosine of angle theta are, respectively:
[tex]\cos \theta = -\frac{11}{61}[/tex]
[tex]\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}[/tex]
[tex]\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}[/tex]
99 points for brainliest
Answer:
144
Step-by-step explanation:
4 triangles = 1/2 x 6 x 9 x 4 = 108
1 sq base = 6 x 6 = 36
total surface area = 36 + 108 = 144
if 3 triangles the base wouldn't be a square thus not possible to solve
Answer:
144
Step-by-step explanation:
SA = Area of base + 4 area of triangles
6² + 4(9 × 6 × 1/2)
36 + 4(27)
= 144
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
JLK = 360-154 (Circle is 360°)
So
JLK = 206
c^2 = a^2 + b^2 - 2ab cos C make cos C the subject of the formula
Answer:
[tex]\frac{c^{2}-a^{2}-b^{2} }{-2ab}[/tex]=cos C
Step-by-step explanation:
Start with the parts that are more loosely attached to the cos C: the a² and the b², they are only attached with addition, which can be easily undone by subtracting from both sides. That gives you c²-a²-b²=-2abC
Next, since you want to isolate cosC, you will want to divide by everything attached to the cosC by multiplication: (c²-a²-b²)÷(-2ab)=cosC. Then you can neaten it up and put it in fraction form: [tex]\frac{c^{2}-a^{2}-b^{2} }{-2ab}[/tex]=cos C
N
2) A sample of size n= 49 is obtained. The population mean
is m= 80 and the population standard deviation is s = 14.
Find the probability that the sample has a sample average
between 78.3 and 85.1, (5 points)
-
Answer:
0.7969
Step-by-step explanation:
Given that: A sample of size n= 49 is obtained. The population mean is m= 80 and the population standard deviation is s = 14.
The z score measures the number of standard deviation by which the raw sore is above or below the mean. It is given by the equation:
[tex]z=\frac{x-m}{\frac{s}{\sqrt{n} } }[/tex]
For x = 78.3, the z score is:
[tex]z=\frac{x-m}{\frac{s}{\sqrt{n} } }=\frac{78.3-80}{\frac{14}{\sqrt{49} } } =-0.85[/tex]
For x = 85.1, the z score is:
[tex]z=\frac{x-m}{\frac{s}{\sqrt{n} } }=\frac{85.1-80}{\frac{14}{\sqrt{49} } } =2.55[/tex]
P(78.3<x<85.1) = P(-0.85<z<2.55) = P(z<2.55) - P(z<-0.85) = 0.9946 - 0.1977 = 0.7969
Answer:
P(78.3 < x' < 85.1) = 0.7969
Step-by-step explanation:
Given:
Sample size, n = 49
mean, u = 80
Standard deviation [tex] \sigma [/tex] = 14
Sample mean, ux' = population mean = 80
Let's find the sample standard deviation using the formula:
[tex] \sigma \bar x = \frac{\sigma}{\sqrt{n}} [/tex]
[tex] = \frac{14}{\sqrt{49}} = \frac{14}{7} = 2 [/tex]
To find the probability that the sample has a sample average between 78.3 and 85.1, we have:
[tex] P(78.3 < \bar x < 85.1) = \frac{P[(78.3 -80)}{2} < \frac{(\bar x - u \bar x)}{\sigma \bar x} < \frac{(85.1 -80)}{2}] [/tex]
= P( -0.85 < Z < 2.55 )
= P(Z < 2.55) - P(Z <-0.85 )
Using the standard normal table, we have:
= 0.9946 - 0.1977 = 0.7969
Approximately 0.80
Therefore, the probability that the sample has a sample average between 78.3 and 85.1 is 0.7969
The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let ? = 0.05
What is the test statistic for this test?
Answer:
The test statistic for this test is 3.82.
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 8500[/tex]
The alternate hypotesis is:
[tex]H_{1} > 8500[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]X = 8745, \mu = 8500, \sigma = 1200, n = 350[/tex]
So
[tex]t = \frac{8745 - 8500}{\frac{1200}{\sqrt{350}}} = 3.82[/tex]
The test statistic for this test is 3.82.
