The average return for large-cap domestic stock funds over the three years 2009–2011 was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.6%. a.  What is the probability an individual large-cap domestic stock fund had a three-year return of at least 20% (to 4 decimals)?

{Exercise 6.17}

1. The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket (Bureau of Transportation Statistics website, November 2, 2012). Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $110.

a.  What is the probability that a domestic airfare is $550 or more (to 4 decimals)?

b.  What is the probability that a domestic airfare is $250 or less (to 4 decimals)?

c.  What if the probability that a domestic airfare is between $300 and $500 (to 4 decimals)?

d.  What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)
$ or  – Select your answer – more less Item 5

{Exercise 6.18 (Algorithmic)}

2. The average return for large-cap domestic stock funds over the three years 2009–2011 was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.6%.

a.  What is the probability an individual large-cap domestic stock fund had a three-year return of at least 20% (to 4 decimals)?

b.  What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less (to 4 decimals)?

c.  How big does the return have to be to put a domestic stock fund in the top 10% for the three-year period (to 2 decimals)?
%

{Exercise 6.23 (Algorithmic)}

3. The time needed to complete a final examination in a particular college course is normally distributed with a mean of 79 minutes and a standard deviation of 8 minutes. Answer the following questions.

a.     What is the probability of completing the exam in one hour or less (to 4 decimals)?
b.    What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?
c.     Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to 2 decimals)?

4. {Exercise 6.9}

A random variable is normally distributed with a mean of μ = 50 and a standard deviation of σ = 5.

a.     What is the probability that the random variable will assume a value between 45 and 55 (to 3 decimals)?
b.    What is the probability that the random variable will assume a value between 40 and 60 (to 3 decimals)?