Answer:
Step-by-step explanation:
Hello!
There was a special program funded, designed to reduce crime in 8 areas of Miami.
The number of crimes per area was recorded before and after the program was established in each area. This is an example of a paired data situation. For each are in Miami you have recorded a pair of values:
X₁: Number of crimes recorded in one of the eight areas of Miami before applying the special program.
X₂: Number of crimes recorded in one of the eight areas of Miami after applying the special program.
Area: (Before; After)
A: (14; 2)
B: (7; 7)
C; (4; 3)
D: (5; 6)
E: (17; 8)
F: (12; 13)
G: (8; 3)
H; (9; 5)
To apply a paired sample test you have to define the variable "difference":
Xd= X₁ - X₂
I'll define it as the difference between the crime rate before the program and after the program.
If the original populations have a normal distribution, we can assume that the variable defined from them will also have a normal distribution.
Xd~N(μd; σd²)
If the crime rate decreased after the special program started, you'd expect the population mean of the difference between the crime rates before and after the program started to be less than zero, symbolically μd<0
The hypotheses are:
H₀: μd≥0
H₁: μd<0
α: 0.01
[tex]t= \frac{X[bar]_d-Mu_d}{\frac{S_d}{\sqrt{n} } } ~~t_{n-1}[/tex]
To calculate the sample mean and standard deviation of the variable difference, you have to calculate the difference between each value of each pair:
A= 14 - 2= 12
B= 7 - 7= 0
C= 4 - 3= 1
D= 5 - 6= -1
E= 17 - 8= 9
F= 12 - 13= -1
G= 8 - 3= 5
H= 9 - 5= 4
∑Xdi= 12 + 0 + 1 + (-1) + 9 + (-1) + 5 + 4= 29
∑Xdi²= 12²+0²+1²+1²+9²+1²+5²4²= 269
X[bar]d= 29/8= 3.625= 3.63
[tex]S_d=\sqrt{\frac{1}{n-1}[sumX_d^2-\frac{(sumX_d)^2}{n} ] } = \sqrt{\frac{1}{7}[269-\frac{29^2}{8} ] } = 4.84[/tex]
[tex]t_{H_0}= \frac{3.63-0}{\frac{4.86}{\sqrt{8} } } = 2.11[/tex]
This test is one-tailed to the left and so is the p-value, under a t with n-1= 8-1=7 degrees of freedom, the probability of obtaining a value as extreme as the calculated value is:
P(t₇≤-2.11)= 0.0364
The p-value is greater than the significance level, so the decision is to not reject the null hypothesis. Then at a 1% significance level, you can conclude that the special program didn't reduce the crime rate in the 8 designated areas of Miami.
I hope it helps!
Using the t-distribution, it is found that since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.
At the null hypothesis, it is tested if there has been no reduction, that is, the subtraction of the mean after by the mean before is at least 0, hence:
[tex]H_0: \mu_A - \mu_B \geq 0[/tex]
At the alternative hypothesis, it is tested if there has been a reduction, that is, the subtraction of the mean after by the mean before is negative, hence:
[tex]H_1: \mu_A - \mu_B < 0[/tex]
For both before and after, the mean, standard deviation of the sample(this is why the t-distribution is used) and sample sizes are given by:
[tex]\mu_B = 9.5, s_B = 4.504, n_B = 8[/tex]
[tex]\mu_A = 5.875, s_A = 3.5632, n_A = 8[/tex]
The standard errors are given by:
[tex]s_A = \frac{3.5632}{\sqrt{8}} = 1.2596[/tex]
[tex]s_B = \frac{4.504}{\sqrt{8}} = 1.5924[/tex]
For the distribution of differences, the mean and standard error are given by:
[tex]\overline{x} = \mu_A - \mu_B = 5.875 - 9.5 = -3.625[/tex]
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{1.2596^2 + 1.5924^2} = 2.0304[/tex]
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.Hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{-3.625 - 0}{2.0304}[/tex]
[tex]t = -1.7854[/tex]
The p-value is found using a t-distribution calculator, with t = -1.7854, 8 + 8 - 2 = 14 df and a left-tailed test with a significance level of 0.01, as we are tested if the mean is less than a value.
Using the calculator, the p-value is given by 0.048.Since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.
You can learn more about the use of the t-distribution to test an hypothesis at https://brainly.com/question/13873630
Find the value of x needed to make the equation below true.
Step-by-step explanation:
[tex]5(2x - 4) = 2(4x + 2) \\ 10x - 20 = 8x + 4 \\ 2x = 24 \\ x = 12[/tex]
Simplify –2x3y × xy2.
Question 1 options:
A)
–3x4y3
B)
–2x4y3
C)
–2x3y4
D)
–12x4y3
Answer: B. -2x^4y^3
Step-by-step explanation:
Multiply the variables by each other.
-2x^3 * x = -2x^4
y * y^2 = y^3
Answer:
B) -2x4y3
Step-by-step explanation:
Cuanto es 1× -1× es x o no?
Answer:
[tex]1^x[/tex] is always 1, so [tex]1^x-1^x=0[/tex]
es0
dame grasias
si soi nuevo
A nursery located in Florida uses a water meter to measure its water usage 1 point
in CCF. It is charged $0.36 per CCF of water. Its last meter reading was
123,692 and their present reading is 127,394. For this usage, the nursery was
charged $332.72*
True or false?
Answer:
Step-by-step explanation:
From the information given, their last meter reading was 123,692 and their present reading is 127,394. The difference between the last and the present meter reading is
127394 - 123692 = 3702
If the water meter measures its water usage in terms of 1 point in CCF, then the amount of CCF of water used is 3702. If the school is charged $0.36 per CCF of water, then for this usage, the charge would be
3702 × 0.36 = $1332.72
Therefore, it is false
5. A cyclist and bike have a total mass of 102 kg and a speed of 17 m/s.calculate the kinetic energy?
Answer:
14739
Step-by-step explanation:
1/2mv^2
1/2*105*17*17
=14739
which of the following questions are identities? Check all that apply
Answer:
all I see is a black image
question is attached
Answer:
The centroid is 1/3 of the vertical distance between QV
QV = 3 x VT = 3 x 5 = 15
QT = 15-5 = 10
what should be add to 7 3/5 to get 18
Answer:
[tex]10\frac{2}{5}[/tex]
Step-by-step explanation:
[tex]7\frac{3}{5} + x = 18\\[/tex]
transformation : [tex]7\frac{3}{5} = \frac{(5*7) + 3}{5} = \frac{38}{5}[/tex]
[tex]\frac{38}{5} + x = 18\\\\x = 18 - \frac{38}{5} = \frac{(5*18) - 38}{5} = \frac{52}{5}[/tex]
[tex]\frac{52}{5} = 10\frac{2}{5}[/tex]
Answer:
[tex]10\frac{2}{5}[/tex]
Step-by-step explanation:
What should be add to [tex]7\frac{3}{5}[/tex] to get [tex]18[/tex] ?
[tex]18-7\frac{3}{5}=\\ \\=17\frac{5}{5}-7\frac{3}{5}\\\\\\=(17-7)+(\frac{5}{5}- \frac{3}{5})\\ \\=10+\frac{2}{5}\\ \\=10\frac{2}{5}[/tex]
Can someone please explain how to
find the mean , median , range, and interquartile range????
A study will be conducted to examine a new medicine intended to reduce high blood pressure in adult men who have high blood pressure. As part of the study, a random sample of 40 men with high blood pressure will have their blood pressure measured, and then they will take the new medicine every day for one month. At the end of the month, their blood pressure will be measured again. Of the following, which is the best procedure to investigate whether there will be convincing statistical evidence of a change, on average, in blood pressure for men with high blood pressure who take the new medicine? (A) A one-sample z-test for a proportion (B) A two-sample z-test for a difference between proportions (C) A two-sample i-test for the difference between two means (D) A matched-pairs t-test for a mean difference (E) A chi-square test of independence
Answer:
Option D
Step-by-step explanation:
A matched pairs t-test is appropriate for this experiment. It compares two means that are from the same individual; the before drug administration and the after drug administration. It compares the before-and-after observations on the same subjects.
The best and convincing statistical evidence of a change, on average, in blood pressure is the t test.
What is t test?The test is one of the kinds of inferential statistics. It is deployed in decision making. As such, it involves the test to see if there is significant difference between the means of two groups, which may be related.
Hence, in this study, the best and convincing statistical evidence of a change, on average, in blood pressure is the t test.
Learn more about t test:https://brainly.com/question/15870238
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. The graph cross the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10
Step-by-step explanation:
→Looking at the line as it increases, you can see that it intersects at the point of (0, 5) on the y-axis.
→The line on the graph is increasing from the point where x = -10, and stops at x = 2.
→The line then stays constant (basically meaning it doesn't increase/decrease, making it a horizontal line), strting from x = 2, to x = 10.
Looking at the points above, you can determine that the correct answer is "B. The graph cross the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10."
Jenny has $20 in a savings account. The interest rate is 5% compounded annually. To the nearest cent, how much interest will she earn in 2 years?
Answer:
22.05
Step-by-step explanation:
3x - 7 = 8 looking for the answer to X
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
[tex]3x - 7 = 8[/tex]
[tex]3x = 8+7[/tex]
[tex]3x=15[/tex]
[tex]x=5[/tex]
Answer:
x=5
Step-by-step explanation:
Let's solve your equation step-by-step.
3x−7=8
Step 1: Add 7 to both sides.
3x−7+7=8+7
3x=15
Step 2: Divide both sides by 3.
3x/3=15/3
x=5
The sum of x and it’s opposite is always zero?
Answer:
1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies
2) Now let's consider any real number a no matter positive or negative we will have that:
[tex]a-a =0[/tex]
Or in the other case:
[tex]-a -(-a) =-a +a=0[/tex]
So then we can conclude that the expression is a general rule and is true
Step-by-step explanation:
For this case we can verify if the following expression is true or false:
The sum of x and it’s opposite is always zero?
If we want to proof this we need to show that for any number is true.
1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies
2) Now let's consider any real number a no matter positive or negative we will have that:
[tex]a-a =0[/tex]
Or in the other case:
[tex]-a -(-a) =-a +a=0[/tex]
So then we can conclude that the expression is a general rule and is true
After several shares of the company stock was sold, a profit of $1320 was earned. The prophet was over 15% over 30 day period. How much were the shares worth when they were originally purchased
Answer:
$104430
Step-by-step explanation:
Let's recall the formula
PRT/100 = interest I
Where
P = principal/initial amount
R = rate
T= period or time
P =( 100*I)/(RT)
P =( 100*1320)/(15*(30/356))
P = 132000/1.264
P = $104430
Given that y varies directly with x, use the values specified to write a
direct variation equation relating y to x.
x = -19, y = 190
Use your answer to find x when y = -9.
Answer:
(a)y=-10x
(b)x=0.9
Step-by-step explanation:
If y varies directly with x, we write:
[tex]y \propto x\\y=kx$ where k is the constant of proportionality.\\If $x = -19, y = 190\\190=-19k\\$Divide both sides by -19\\k=190 \div -19\\k=-10\\[/tex]
Therefore, a direct variation equation relating y to x is:
(a)y=-10x
(b)When y=-9
Substituting y=-9 into the equation obtained in (a) above
[tex]-9=-10x\\$Divide both sides by -10$\\x=-9\div -10\\x=0.9\\$Therefore, when $ y=-9, x=0.9[/tex]
Mice and Pain Can you tell if a mouse is in pain by looking at its facial expression? A new study believes you can. The study1 created a "mouse grimace scale" and tested to see if there was a positive correlation between scores on that scale and the degree and duration of pain (based on injections of a weak and mildly painful solution.) The study's authors believe that if the scale applies to other mammals as well, it could help veterinarians test how well painkillers and other medications work in animals. 1"Of Mice and Pain", The Week, May 28, 2010, p. 21. 1. State the null and alternative hypotheses. 2.Since the study authors report that you can tell if a mouse is in pain by looking at its facial expression, do you think the data were found to be statistically significant? 3.If another study were conducted testing the correlation between scores on the "mouse grimace scale" and a placebo (non-painful) solution, should we expect to see a sample correlation as extreme as that found in the original study? 4. If another study were conducted testing the correlation between scores on the "mouse grimace scale" and a placebo (non-painful) solution, should we expect to see a sample correlation as extreme as that found in the original study, if the original study results showed no evidence of a relationship between mouse grimaces and pain?
Explanation:
1. a) Null hypothesis: There is no statistically significant relationship between the mouse grimace scale and the amount of pain felt by mouse.
b) Alternate hypothesis: There is a statistically-significant relationship between the mouse grimace scale and the amount of pain felt by mouse.
2. Yes, because a statistically significant data implies that there is sufficient evidence to believe the study, based on the results of the findings.
3. No, since the variables are different in this case. Here we are dealing with a non-painful solution so there may be no sample correlation as extreme as that found in the original study.
4. Possibly, because every hypothesis is an assumption until it is proven. Thus, in every statistical research, there may be different findings.
Which of the following is the absolute value parent function? A. F(X) = | x | + 1
B. F(x) = x^2
C. F(x) = | x |
D. F(x) = 1/x
Answer:
C. F(x) = | x |
Step-by-step explanation:
The parent function has no adornments, shifts, multipliers, offsets, reflections, or anything else.
The absolute value of x is written |x|. That is the parent absolute value function.
F(x) = |x|
Answer: C
Step-by-step explanation:
What factoring method should be used to factor a polynomial with four terms?
Answer:
The easiest way to factor it is to use grouping.
Step-by-step explanation:
you look at only two terms at a time to see if any techniques become apparent.
The grouping factoring method should be used to factor a polynomial with four terms.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The simplest method to factor a polynomial with four or more parts is to use grouping. With this approach, you evaluate just two terms at once to determine whether any methods stand out.
Therefore, the grouping factoring method should be used to factor a polynomial with four terms.
Learn more about the polynomial here:
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My rule is: y= 1/3x+ 11/15 Find x, if y=1.
Answer:
x=5/4
Step-by-step explanation:
First, plug in 1 for y. Since a common denominator for the right side is 3, multiply both sides by 3 to get 3=x+11/5. Then multiply both sides by 5 to get 15=5x+11. Subtract 11 on both sides to get 4=5x. Finally divide by 5 to get x by itself and get x = 5/4.
What is the sum of V-2 and V-18?
Answer:
=2v−20
Step-by-step explanation:
Let's simplify step-by-step.
v−2+v−18
=v+−2+v+−18
Combine Like Terms:
=v+−2+v+−18
=(v+v)+(−2+−18)
=2v+−20
Answer:
=2v−20
Use long division to find quotient below
the answer is in the photos
Mrs. Beverly brought two quarts of juice to class.
How many cups of juice could she pour for the students?
Answer:
8
Step-by-step explanation:
1 quart=4 cups so 4x2=8
Find the perimeter of the figure 35 in. 34 in. 70 in. 84 in.
Answer:
p=8in+8in+12in+7in
=35 in
Answer:
35
Step-by-step explanation:
a bag contains 8 red balls and 6 green balls. michelle randomly draws 3 balls from the bag. she does not replace the balls after each draw. what is the probability that she draws 2 red balls and 1 green ball
Answer:
Red balls 2/14
Green balls 1/14
Step-by-step explanation:
I hope that helped.
please help plzzzzzzzzzzzzzzzzzzzz
Answer: C,D are true
Step-by-step explanation:
Answer:
Step-by-step explanation:
C and D are both true the rest are false
7×{(-150)÷(10-10-5)}
Answer:
[tex]=210[/tex]
Step-by-step explanation:
[tex]7\times \left(-150\right)\div \left(10-10-5\right)\\Follow\:the\:PEMDAS\:order\:of\:operations\\\mathrm{Calculate\:within\:parentheses}\:\left(10-10-5\right)\::\quad -5\\10-10-5\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\\10-10=0\\=0-5\\=0-5\\=-5\\=7\times \left(-150\right)\div \left(-5\right)\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:7\times \left(-150\right)\div \left(-5\right)\::\quad 210\\7\times \left(-150\right)\div \left(-5\right)[/tex]
[tex]\mathrm{Apply\:rule\:}-a\div \left(-b\right)\:=\:a\div \:b\\-1050\div \left(-5\right)=1050\div \:5=210\\=210[/tex]
Answer:
210
Step-by-step explanation:
7×{(-150)÷(10-10-5)}
remove the opposites
7×{(-150)÷(-5)}
divide
7×30
multiply
210
Another question (sorry)
Answer:
19.99
Step-by-step explanation:
First you would multiply .44 by 16 to get 7.04
then you would add 12.95 to get 19.99
The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.3 years, with a standard deviation of 3.4 years. The winner in one recent year was 22 years old.
(a) Transform the age to a z-score.
(b) Interpret the results.
(c) Determine whether the age is unusual.
Answer:
Convert the age to a z-score:
Step-by-step explanation:
Let X be the random variable with mean 27.2 and standard deviation 3.8.
Here, the observation, x is 24.
The z-score of the winner's age is -1.56.
A negative z-score indicates that the value is below the mean.
The age of the winner is not considered unusual.
What is z-score?
A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.
It measures the unusual or extreme a particular data point is compared to the rest of the distribution
We have,
(a)
To transform the age of the winner into a z-score, we use the formula:
z = (x - μ) / σ
where x is the value we want to transform, μ is the mean, and σ is the standard deviation.
So,
Substituting the values given,
z = (22 - 27.3) / 3.4
z = -1.56
The z-score of the winner's age is -1.56.
(b)
A z-score represents the number of standard deviations a data point is from the mean.
In this case, the winner's age is 1.56 standard deviations below the mean age of the winners.
A negative z-score indicates that the value is below the mean.
(c)
Compare the z-score to a threshold value.
A commonly used threshold for unusual values is z = ±2.
If the absolute value of the z-score is greater than or equal to 2, then the value is considered unusual.
So,
The absolute value of the z-score is less than 2 (|z| < 2), which means that the age of the winner is not considered unusual in the context of the distribution of the ages of the winners.
Thus,
The z-score of the winner's age is -1.56.
A negative z-score indicates that the value is below the mean.
The age of the winner is not considered unusual.
Learn more about z-score here:
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The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.80. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.25 and P(B | A2) = 0.05. (a) Are A1 and A2 mutually exclusive? They mutually exclusive. How could you tell whether or not they are mutually exclusive? P(B | A1) ≠ P(B | A2) P(A1) + P(A2) = 1 P(A1 ∩ A2) = 0 P(A1) ≠ P(A1 | A2) P(A2) ≠ P(A2 | A1) (b) Compute P(A1 ∩ B) and P(A2 ∩ B). P(A1 ∩ B) = P(A2 ∩ B) = (c) Compute P(B). (d) Apply Bayes' theorem to compute P(A1 | B) and P(A2 | B). (Round your answers to four decimal places.) P(A1 | B) = P(A2 | B) =
Answer:
(a) [tex]A_1[/tex] and [tex]A_2[/tex] are indeed mutually-exclusive.
(b) [tex]\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}[/tex], whereas [tex]\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}[/tex].
(c) [tex]\displaystyle P(B) = \frac{9}{100}[/tex].
(d) [tex]\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}[/tex], whereas [tex]P(A_1 \; |\; B) = \displaystyle \frac{4}{9}[/tex]
Step-by-step explanation:
(a)[tex]P(A_1 \; \cap \; A_2) = 0[/tex] means that it is impossible for events [tex]A_1[/tex] and [tex]A_2[/tex] to happen at the same time. Therefore, event [tex]A_1[/tex] and [tex]A_2[/tex] are mutually-exclusive.
(b)By the definition of conditional probability:
[tex]\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}[/tex].
Rearrange to obtain:
[tex]\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}[/tex].
Similarly:
[tex]\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}[/tex].
(c)Note that:
[tex]\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}[/tex].
In other words, [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive. Since [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive and mutually-exclusive at the same time:
[tex]\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}[/tex].
(d)By Bayes' Theorem:
[tex]\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}[/tex].
Similarly:
[tex]\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}[/tex].
Using probability concepts, along with conditional probability and Bayes Theorem, it is found that:
a) [tex]P(A1 \cap A2) = 0[/tex], thus yes, A1 and A2 are mutually exclusive.
b) The probabilities are: P(A1 ∩ B) = 0.05, P(A2 ∩ B) = 0.04.
c) The probability of event B is: P(B) = 0.09.
d) The probabilities are: P(A1|B) = 0.5555 and P(A2|B) = 0.4445.
-----------
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
P(B|A) is the probability of event B given that A. [tex]P(A \cap B)[/tex] is the probability of both A and B. P(A) is the probability of A.-----------
Bayes Theorem:
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
-----------
Item a:
Two events A and B are mutually exclusive if they cannot happen together.Since [tex]P(A1 \cap A2) = 0[/tex], yes, it can be said that events A1 and A2 are mutually exclusive.Item b:
Using conditional probability.
A1 and B:
[tex]P(B|A1) = \frac{P(A1 \cap B)}{P(A1)}[/tex]
[tex]0.25 = \frac{P(A1 \cap B)}{0.2}[/tex]
[tex]P(A1 \cap B) = 0.25(0.2) = 0.05[/tex]
A2 and B:
[tex]P(B|A2) = \frac{P(A2 \cap B)}{P(A2)}[/tex]
[tex]0.05 = \frac{P(A1 \cap B)}{0.8}[/tex]
[tex]P(A1 \cap B) = 0.8(0.05) = 0.04[/tex]
Item c:
P(B) is given by:
[tex]P(B) = P(A1 \cap B) + P(A2 \cap B) = 0.05 + 0.04 = 0.09[/tex]
Item d:
Applying Bayes Theorem
[tex]P(A1|B) = \frac{P(A1)P(B|A1)}{P(B)} = \frac{0.25(0.2)}{0.09} = 0.5555[/tex]
[tex]P(A2|B) = \frac{P(A2)P(B|A2)}{P(B)} = \frac{0.8(0.05)}{9} = 0.4445[/tex]
A similar problem is given at https://brainly.com/question/22428992
