Q2. A certain anti-viral drug is used to cure an infection and the recovery time being
normally distributed with a mean of 28.2 months and standard deviation of 4.2 months. 25
patients who were administered this drug were randomly selected. Now, answer the
following questions with necessary justification.
(Be careful to always first check if conditions are appropriate to answer each question.
Otherwise, do not proceed with calculation.) [2+2+2+2+2+3=13 points]
(a) Compute the mean and standard deviation of the average recovery time of the selected
patients.
(b) Compute the probability that average recovery time of selected patients is between 27
and 29 months.
(c) Compute the probability that the 5-th patient in our sample recovers within 25 months.
(d) Compute the probability that the standard deviation of recovery time of selected
patients is less than 4.5 months.
(e) Compute the probability of occurrence of (b) AND (d).
(f) Compute the probability of occurrence of (b) OR (d).

A daily commuter crosses two traffic signals on his way to work. The probability that he will be stopped at the first signal is 0.47, at the second signal is 0.30, and the probability that he may not have to stop at any of the two signals is 0.3. Answer all the questions to 2 decimal places where appropriate.

1. What is the probability that the commuter will be stopped at both signals?

2. What is the probability that he will be stopped at the second, but not at the first signal?

3. What is the probability that he will be stopped at exactly one signal given that he was not stopped at the first signal?

4. "Stopping at signal 1 is independent of stopping at signal 2." This statement is:
a.Incorrect True because P(stopping at both signals) = P(stopping at signal 1)×P(stopping at signal )
b.ncorrect False because P(stopping at both signals) ≠ 0
c.Incorrect True because P(stopping at both signals) ≠ 0
d.Correct: False because P(stopping at both signals) ≠ P(stopping at signal 1)×P(stopping at signal 2)

1. For each of the following, define the random variable using words, tell what kind of distribution each has, and calculate the probabilities. Every day when Sally drives to school, she has a 70% chance of not finding a parking spot in the closest lot to her classroom (otherwise, she finds a spot). Each day is independent, meaning that finding a spot on one day doesn’t change the probability of finding a spot on any other day.

(a) (3 points) What is the probability that the tenth day is the fifth day that she gets a spot in the closest lot?

(b) (3 points) What is the probability that the tenth day is the first day that she gets a spot in the closest lot?

(c) (3 points) What is the probability that the she gets to park in the closest lot in 5 out of the next 10 days?

(d) (3 points) If she parks in the close lot at least 3 times in a week (5 days), she will treat herself to ice cream. What is the probability that she gets ice cream?

1. Answer the following questions regarding a standard 52-deck, which has 13 of each suite )heart, spades, clubs, and diamonds) and 3 face cards in each suit.

a. What is the probability that you will randomly receive an ace of diamonds or a queen of clubs?

b. If you were to draw a card, replace it, and shuffle, then what would be the probability of drawing the same card again?

c. Face cards are the King, Queen, or Jack cards for each suit. What is the probability of drawing a face card or a diamond card?

2. Dice have 6 sides with 1 through 6 dots on each side. There are 36 possible outcomes with the rolling of two dice. What is the probability that you could roll the sum of 7 with the pair of dice?

3. For a normal distribution with a mean of μ = 50 and σ = 10, find each probability value requested. Show your work in order to receive credit.

a. p(x>65)

b. p(x<47)

c. p(40 < X < 60)

QUESTION FOR ALL - MY MEDIUM IMPACT TRUMPS YOUR HIGH PROBABILITY!

So, we are evaluating our probabilities on an ordinal scale of Very High, High, Medium, Low, Very Low. And we are using the same scale for impacts. A little combinatorial math will tell you that gives us 25 combinations of individual combined ratings.

We know that a Very High probability with a Very High impact will be the top of our list. Likewise, we know a very low probability with a very low impact will be at the bottom. It’s the stuff in the middle that gives us so much problem.

Is a High Probability Medium impact risk a bigger problem than a Medium Probability High impact risk, for example?   We have many of these pairs to sort through if we are going to come up with a combined risk rating for each identified risk.

How do we do that, people? And once we do, how do we document it clearly?

Thoughts, ideas, examples?

help please

{4 marks} Here, we will quickly investigate the importance of understanding conditional prob- abilities when talking with medical patients. This problem is based on a true investigation by Hoffrage and Gigerenzer in 1996. The investigators asked practicing physicians to consider the following scenario:

“The probability that a randomly chosen woman age 40-50 has breast cancer is 1%. If a woman has breast cancer, the probability that she will have a positive mammogram is 80%. However, if a woman does not have breast cancer, the probability she will have a positive mammogram is 10%. Imagine that you are consulted by a woman, age 40-50, who has a positive mammogram but no other symptoms. What is the probability that she actually has breast cancer?”

Twenty-four physicians were asked to respond. The average probability estimate was 70%. Using your knowledge of Bayes’ Rule, determine if the physicians were close in their estimate. Comment on where the error in their judgement may have occurred, and why this may cause problems in their practice.

According to the Current Results website, the state of California has a mean annual rainfall of 23 inches, whereas the state of New York has a mean annual rainfall of 45 inches. Assume that the standard deviation for both states is 3 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. Use z-table. a. Show the probability distribution of the sample mean annual rainfall for California. This is a graph of a normal distribution with E(-/x) and 0x (to 4 decimals). b. What is the probability that the sample mean is within 1 inch of the population mean for California? (to 4 decimals) c. What is the probability that the sample mean is within 1 inch of the population mean for New York? (to 4 decimals) d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why? The probability of being within inch is for New York in part (c) because the sample size is

1) Consider the discrete probability distribution to the right when answering the following question. Find the probability that x exceeds 4.

A) 0.97

b) 0.39

c) 0.58

D) 0.61

2)

The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 15% of people with home-based computers have access to on-line services. Suppose that 12 people with home-based computers were randomly and independently sampled. What is the probability that at least 1 of those sampled have access to on-line services at home?

Question 5 options:

3)

Find the expected value of the random variable. Round to the nearest cent unless stated otherwise.

In a game, you have a  probability of 1/50 winning 106$ and a 49/50 probability of losing 3$. What is your expected value?

Question 7 options:

Thank you!!!!

An institute reported that

68% of its members indicate that lack of ethical culture within financial firms has contributed most to the lack of trust in the financial industry. Suppose that you select a sample of 100 institute members. Complete parts ​(a) through ​(d) below.

a. What is the probability that the sample percentage indicating that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry will be between

66

and 72​%?

0.4704

​(Type an integer or decimal rounded to four decimal places as​ needed.)

b. The probability is 70

that the sample percentage will be contained within what symmetrical limits of the population​ percentage?The probability is 70% that the sample percentage will be contained above 63​%

and below 73%

​(Type integers or decimals rounded to one decimal place as​ needed.)

c. The probability is

97% that the sample percentage will be contained within what symmetrical limits of the population​ percentage? The probability is 97% that the sample percentage will be contained above nothing​% and below nothing​%.

What's the answer to C

1. (a) If A and B are independent events with P(A) = 0.6 and P(B) = 0.7, find P (A or B).

(b) A randomly selected student takes Biology or Math with probability 0.8, takes Biology and Math with probability 0.3, and takes Biology with probability 0.5. Find the probability of taking Math.

2. A box contains 4 blue, 6 red and 8 green chips.

1. In how many different ways can you select 2 blue, 3 red and 5 green chips? (Give the exact numerical value).

2. Draw two chips in a row without replacement. Find the probability that both chips are green.

3. Based on the following table, compute the probabilities below:

P (Women and Yes) =

P (Men | Yes) =

P (No | Women) =

P (Men or No) =

Are Men and No Opinion mutually exclusive?

Are Men and No Opinion independent? Justify your answer by an appropriate computation.