Answer:
1a)Confidence Interval: (77.936,82.064)
b)Confidence Interval: (79.020, 80.980)
c)Confidence Interval: (79.510, 80.490)
d) As the sample size increases, the confidence interval for the lower class (bound) increases while that of the upper class(bound) decreases.
2a)Confidence Interval: (491.609
, 502.797)
b)Confidence Interval: (483.218, 516.782)
c)Confidence Interval: (466.436,533.564)
d)As the standard deviation increases, the confidence interval for the lower class (bound) decreases while that of the upper class(bound) increases.
Step-by-step explanation:
1 a) A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80.
The formula for confidence Interval is:
C.I = Mean ± z score × Standard deviation/√n
Note to apply the formula above n greater than or equal to 30
a) Determine the 95% confidence interval estimate of the population mean.
For a, the confidence interval formula above cannot be applied because n is less than 30, so we use the t score confidence interval value
C.I = Mean ± t score × Standard deviation/√n
Mean = 80
Standard deviation = 5
n = 25
Degree of freedom = 25 - 1 = 24
Hence, 95% confidence interval degree of freedom t score = 2.064
Hence, Confidence Interval =
80 ± 2.064 × 5/√25
80 ± 2.064 × 1
80 ± 2.064
Confidence Interval =
80 - 2.064
= 77.936
80 + 2.064
= 82.064
Confidence Interval: (77.936, 82.064)
b) Repeat part (a) with a sample size of 100.
C.I = Mean ± z score × Standard deviation/√n
Mean = 80
Standard deviation = 5
n = 100
z score for 95% confidence interval = 1.96
C.I = 80 ± 1.96 × 5/√100
C.I = 80 ± 1.96 × 5/10
C.I = 80 ± 1.96 × 0.5
C.I = 80 ± 0.980
Confidence Interval =
80 - 0.980
= 79.020
80 + 0.980
= 80.980
Confidence Interval: (79.020, 80.980)
c) Repeat part (a) with a sample size of 400.
C.I = Mean ± z score × Standard deviation/√n
Mean = 80
Standard deviation = 5
n = 400
z score for 95% confidence interval = 1.96
C.I = 80 ± 1.96 × 5/√400
C.I = 80 ± 1.96 × 5/20
C.I = 80 ± 1.96 × 0.25
C.I = 80 ± 0.490
Confidence Interval =
80 - 0.490
= 79.510
80 + 0.490
= 80.490
Confidence Interval: (79.510, 80.490)
d) As the sample size increases, the confidence interval for the lower class (bound) increases while that of the upper class(bound) decreases.
2a) The mean of a sample of 25 was calculated as ¯x=500. The sample was randomly drawn from a population with a standard deviation of 15.
For a,b and c the confidence interval formula above cannot be applied because n is less than 30, so we use the t score confidence interval value
C.I = Mean ± t score × Standard deviation/√n
a) Mean = 500
Standard deviation = 15
n = 25
Degree of freedom = 25 - 1 = 24
Hence, 99% confidence interval degree of freedom t score = 2.064
Hence, Confidence Interval =
500 ± 2.797 × 15/√25
500 ± 2.797 × 15/5
500 ± 2.797 × 3
Confidence Interval =
500 - 8.391
= 491.609
500 + 8.391
= 508.391
Confidence Interval: (491.609, 508.391)
b) Repeat part (a) changing the population standard deviation to 30
Hence, Confidence Interval =
500 ± 2.797 × 30/√25
500 ± 2.797 × 30/5
500 ± 2.797 × 6
500 ± 16.782
Confidence Interval =
500 - 16.782
= 483.218
500 + 16.782
= 516.782
Confidence Interval: (483.218, 516.782)
c) Repeat part(a) changing to the population standard deviation to 60.
Hence, Confidence Interval =
500 ± 2.797 × 60/√25
500 ± 2.797 × 60/5
500 ± 2.797 × 12
500 ± 33.564
Confidence Interval =
500 - 33.564
= 466.436
500 + 33.564
= 533.564
Confidence Interval: (466.436,533.564)
d)As the standard deviation increases, the confidence interval for the lower class (bound) decreases while that of the upper class(bound) increases.
There are 10 computers and 5 students. How many ways are there for the students to sit at the computers if no computer has more than one student and each student is seated at a computer?
Answer:
30,240 ways
Step-by-step explanation:
This question is bothered on permutation. Permutation has to do with arrangement.
If there are 10 computers and 5 students, the number of ways students will sit at the computers if no computer has more than one student can be expressed as;
10P5 = 10!/(10-5)!
10P5 = 10!/(5)!
10P5 = 10*9*8*7*6*5!/5!
10P5 = 10*9*8*7*6
10P5 = 30,240
Hence the number of ways is 30,240 ways
in the library, there are 9 rectangular tables with 8 pupils each and square tables with 4 pupils each. how many square tables ar needed so that 100 pupils can read at the same time?
Answer:
9 rectangular tables and 7 sqaure tables
Step-by-step explanation:
9 x 8 = 72
100-72=28
4x7=28
2. Adam and Ben are both on diets. Adam currently weighs 210 pounds and is losing 3 pounds per
week. Ben currently weighs 146 pounds and is gaining 5 pounds per week. After how many
weeks will they weigh the same? Either write an equation and solve it, or make a table to come
up with the answer
PLEASE HELP ME QUICK A recipe calls for 4
cups of sugar and 16
cups of water. How
much water is needed
if you only have I cup
of sugar?
Answer:4
Step-by-step explanation:if you only have one cup of sugar you will have to propitiate the rest so just divide 16 by 4 to get 4
The product of -5 and a number is at least -40
Please help and explain how you got your answer I will give brainliest :(
Answer:
25/100 or 1/4
Step-by-step explanation:
the 2 shaded rows on the top are both 10 and the bottom shaded row is 5 so the equation would be 2×10+5
Answer:
0.25
Step-by-step explanation:
The model represents one whole number (1)
Each square represents .01 of the whole number.
So if you add all the shaded squares together, you would get 25 shaded, which means the answer would be 0.25
hope this helps :)
Find the missing value in the ratio table.
100000000000000000000
I need help plz!!!!
Write an inequality for the following statement. A is greater than 7
Answer: A>7
Step-by-step explanation:
Order the numbers from least to greatest.
4/5, -1.6, -4/3, 0.9, 2/3
PLS HELP
Answer:
-1,6<-4/3<2/3<4/5<0.9
Step-by-step explanation:
What is the correctly factors for the expression 24xy-15y
Answer:
4.0/5
Step-by-step explanation:
- She divided by 3 instead of the GCF.
- She didn’t complete step 4 and use the distributive property to be sure the expressions are equivalent.
- She didn’t undistributed the GCF from the original expression.
Write the equation of a line that safely lands the plane. Press submit to see if the plane lands safely.
Answer:
[tex] y = \frac{3}{4}x - \frac{1}{4} [/tex]
Step-by-step explanation:
First, find the slope using the points (3, 2) and (-1, -1):
Slope = [tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 2}{-1 - 3} = \frac{-3}{-4} = \frac{3}{4} [/tex]
Find the y-intercept, b, by substituting x = -1, y = -1 and m = ¾ in y = mx + b.
-1 = ¾(-1) + b
-1 = -¾ + b
Add ¾ to both sides
-1 + ¾ = b
(-4 + 3)/4 = b
-¼ = b
Substitute m = ¾ and b = -¼ in y = mx + b.
The equation would be:
✅[tex] y = \frac{3}{4}x - \frac{1}{4} [/tex]
You pay 6% sales tax on a $250 purchase. How much was the tax?
Answer:
15
Step-by-step explanation:
To find the tax multiply the cost of the item by 6%
250 * 6%
Change to decimal form
250 *.06
15
Answer:
15
Step-by-step explanation:
convert the percentage to a decimal
6/100 = 0.06
then times by the number you given
6% x 250
What are the clear steps for solving for x question (5x + 2)
Answer:
x= -2/5
Step-by-step explanation:
(5x+2)=0
-2 -2
5x=-2
------------
5
x= -2/5
A) complementary
B) alternate exterior
C) corresponding
D) linear pair
I'll give brainliest if you answerrr! A seesaw is in balance when a weight times its distance on one side of the fulcrum is equal to another weight times its distance on the other side of the fulcrum. In the diagram, the 20-lb. weight is 5 feet from the fulcrum and another weight is 8 feet from the fulcrum. Using the in-balance seesaw shown, find the number of pounds in the weight represented by N.
Answer:
12.5
Step-by-step explanation:
The 20 lbs on the left side time the 5 feet is equal to 100.
You need the weight on the right side to equal 100 when it is multiplied to it's length from the fulcrum, which is 8.
All you need to do is divide 100 by 8, to get 12.5.
please help I need in within 5 minutes
Answer:
2415.8
Step-by-step explanation:
Answer: 2509.8 i think that is the correct answer
Step-by-step explanation:
The length of one side of a square is 3n+2. The perimeter of the square is 4(3n+2). Which expression is equivalent to the perimeter
Answer:
4(3n + 2)
Step-by-step explanation:
as we know perimeter of a square is 4 x side
one side is 3n + 2
4 sides = 4(3n +2)
A hot air balloon is climbing at a constant rate into the sky. The equation y = 9x + 10 can be used to represent this situation, where y is the height of the hot air balloon in feet above ground and x is the number of seconds the balloon has been climbing.
Answer:
From the starting position of 10 feet above ground, the balloon is climbing 9 feet per second.
Step-by-step explanation:
Determine the slope and y-intercept.
Answer: Your y-intercept form is -3 which is written b= -3
Your slope is 1/2 written like m= 1/2
Step-by-step explanation: Here is the eqaution!
y=1/2x-3
I hope this helps
btw can i have brainliest?
Favorite Lunch Choice
Food Responses
pizza 26
hamburger 18
chicken 13
nachos 7
spaghetti 6
If there are 350 students in Jamal's school, how many are expected to choose hamburgers?
O A. 180 students
OB. 130 students
OC. 90 students
O D. 18 students
Convert to slope intercept form: 3x-4y=8 then graph the line on the grid
Answer:
y=3/4x-2
a=(8/3,0)
b=(0,-2)
m=3/4
Step-by-step explanation:
STEP 1
3x-4y =8 substract 3x from both sides
-4y=-3x+8 divide -4 to everything
y=3/4x-2
STEP 2
substitute 0 for y and solve for a (x-intercept)
X/4 -3 = 1/3 + 2x solve for x
Answer:
Step-by-step explanation:
[tex]\frac{x}{4}[/tex] - 3 = [tex]\frac{1}{3}[/tex] + 2x ...... (1)
(1) × 12 :
3x - 36 = 4 + 24x
21x = - 40
x = - [tex]\frac{40}{21}[/tex] = [tex]-1\frac{19}{21}[/tex]
Jason invests $325 in a bank account. The bank has an annual
interest rate of 24%. How much interest did his investment earn
after one year?
The amount of interest earned by Jason is $78.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.
Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.
Given that Jason invests $325 in a bank account. The bank has an annual interest rate of 24%.
The interest will be calculated as:-
SI = ( P x R x T ) / 100
SI = ( 325 x 24 x 1 ) 100
SI = $78
Hence, the simple interest is $78.
To know more about simple interests follow
https://brainly.com/question/25793394
#SPJ2
Write an equation of the line that passes through (1, 2) and is perpendicular to the line y =1/3x + 4.
Answer:
y= -3x + 5
Step-by-step explanation:
negative reciprocial of the slope:
m=1/3
m=-3
Subsitube the point (1,2) into y=mx+b with new slope and solve for b:
y=mx+b
2=-3(1)+b
b=5
Equation:
y=-3x+5
In 8 years, Sophia's age will be 21 years old. Let x represent Sophia's current
age today.
a. Write an equation that can be used to find Sophia's age today (X). [1 point)
b. Solve for x to find Sophia's age. [1 point)
Answer:
a. x+8=21
b. x = 13
Step-by-step explanation:
Answer:
She is 13 years old
Step-by-step explanation:
x + 8 = 21
x = 13
Inflation and Interest Rates: Tutorial
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Question
Consider a simple economy where the basket of goods used to calculate the CPI contains two items shampoo and soap.
The basket consists of 1 bottle of shampoo and 2 bars of soap. The prices are shown in the table.
Year Price of a Bottle of Shampoo Price of a Bar of Soap
Year
36 50
$1.25
Year
$5.00
$1.30
Type the correct answer in the box. Round your answers to two decimal places, if necessary.
The CPI for year 2 is
Submit
Answer:102.22
Step-by-step explanation:
Answer:
2.22%
Step-by-step explanation:
Recall that year 1, the base year, has a CPI of 100.
From question 1, we know that the CPI of year 2 is 102.22.
To find the rate of inflation, find the percent change from year 1 to year 2:
102.22-100= 0.0222, or 2.22%
_________
100
Amita's kitchen is rectangular with an area of 3 and 3/4 square meters the width of the kitchen is 1 and 1/2 m what is the length in meters of Anita's kicthen
Answer:
2 1 ÷ 2
Step-by-step explanation:
Given that
The kitchen of Amita would be a rectangular area contains 3 and 3 ÷ 4 square meters
And, the width of her kitchen is 1 and 1 ÷ 2 meter
So based on the above information, the length of Amita kitchen is
Here you divide the rectangular area by the width
= (3 and 3 ÷ 4) ÷ (1 and 1 ÷ 2)
= 2 and 1 ÷ 2
Hence, the length in meters of Anita's kitchen is 2 and 1 ÷ 2
What is the mean of the set below? Round to the nearest tenths if need be. * Goals in a Hockey Game 2 3 3 3 4 5 5 5 5 6 7 8
Answer:
5-
I think its 5...
Evaluate the expression x(2y+3z) when x=8, y=3, and z=2.
