It's technically senior high school level going on to College.Module 3 V. Demydovych, Summer 2021...

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It's technically senior high school level going on to College.Module 3 V. Demydovych, Summer 2021 Module 3 Assignment 1. Consider the following discrete probability distribution: x -25 -15 10 20 P(X=x) 0.35 0.10 0.10 (a) Complete the probability distribution. (b) Graphically depict the probability distribution and comment on the symmetry of the distri- bution. (c) What is the probability that the random variable X is negative? (d) What is the probability that the random variable X is greater than -20? (e) What is the probability that the random variable X is less than 20? 2. A financial analyst creates the following probability distribution for the performance of an equity income mutual fund. Performance Numerical Score Probability Very poor 1 0.14 Poor 2 0.43 Neutral 3 0.22 Good 4 0.16 Very good 5 0.05 (a) Comment on the optimism or pessimism depicted in the analyst’s estimates. (b) Convert the above probability distribution to a cumulative probability distribution. (c) What is the probability that this mutual fund will do at least ”Good”? 3. Four years ago, Victor purchased a very reliable automobile (as rated by a reputable consumer advocacy publication). His warranty has just expired, but the manufacturer has just offered him a 5-years, bumper-to-bumper warranty extension. The warranty costs $3,400. Victor constructs the following probability distribution with respect to anticipated costs if he chooses not to purchase the extended warranty. Cost in $ Probability 1,000 0.25 2,000 0.45 5,000 0.20 10,000 0.10 (a) Calculate Victor’s expected cost. (b) Given your answer in a part a, should Victor purchase the extended warranty? (Assume risk neutrality.) Explain. 4. Assume that X is a binomial random variable with n=8 and p=0.32. Calculate the following probabilities: (a) P (3  1.32) (b) P (Z ≤ −1.32) (c) P (1.32 ≤ Z ≤ 2.37) (d) P (−1.32 ≤ Z ≤ 2.37) 10. Find the following z values for the standard normal variable Z. (a) P (Z ≤ z) = 0.1020 (b) P (z ≤ Z ≤ 0) = 0.1772 (c) P (Z > z) = 0.9929 Module 3 V. Demydovych, Summer 2021 (d) P (0.40 ≤ Z ≤ z) = 0.3368 11. Assume that IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 16. Use the empirical rule for normal distribution to answer the following questions. (a) What percentage of people score between 84 and 116? (b) What percentage of people score less than 68? 12. Americans are increasingly skimming on their sleep. A health expert believes that American adults sleep an average of 6.2 hours on weekdays with a standard deviation of 1.2 hours. To answer the following questions, assume that sleep time on weekdays is normally distributed. (a) What percentage of American adults sleep more than 8 hours on weekdays? (b) What percentage of American adults sleep less than 6 hours on weekdays? (c) What percentage of American adults sleep between 6 and 8 hours on weekdays? 13. According to a recent survey, high school girls average 100 text messages daily. Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken. (a) What is the probability that the sample mean is more than 105? (b) What is the probability that the sample mean is less than 95? (c) What is the probability that the sample mean is between 95 and 105? 14. Europeans are increasingly upset at their leaders for making deep budget cuts to many social programs that are becoming to expensive to sustain. For instance, the popularity of then President Nicolas Sarkozy of France plummeted in 2010, giving him an approval rating of just 26%. (a) What is the probability that fewer than 60 of 200 French people gave President Sarkozy a favorable rating? (b) What is the probability that more than 150 of 200 French people gave President Sarkozy an unfavorable rating?

Subhanbasha · Accepted Answer

Answers 
1.
a).
Ans: 
The total probability is equal to 1
Therefore ∑ P(X) =1
Let a be the unknown probability of where x= 10
0.35+0.10+a+0.10 = 1
  a = 0.45
	x
	-25
	-15
	10
	20
	p(X=x)
	0.35
	0.1
	0.45
	0.1
b).
Ans:
The above plot showing that the distribution is not symmetrical.
c).
Ans:
P (X is negative) = 0.35+0.10 =0.45
d).
Ans: P (X is greater than -20) =0.10+0.45+0.10 = 0.65
P (X >-20) = 0.65
e).
Ans:
P (X is greater than -20) =0.35+0.10+0.45 = 0.9
P (X 14) = 0.

Module 3 V. Demydovych, Summer 2021 Module 3 Assignment 1. Consider the following discrete probability distribution: x XXXXXXXXXX P(X=x XXXXXXXXXX (a) Complete the probability distribution. (b)...

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