Question#1

a. A report from Center for Health Statistics says that the height of a 20-year-old men when chosen at random,  is a random variable (RV) X with mean height of 5.8 feet and standard deviation 0.24 feet.  Height is "normally" distributed.

Find the mean and standard deviation of the height in inches of a randomly selected 20-year old men. (Note: There are 12 inches in a foot)

Calculate the 90th percentile for the height of 20 year old men.

Calculate the probability that the man is taller than 5' 11" tall.

b. Ms. Newell gave her class a 10-question multiple-choice quiz with 4 choices. Let X = the number of questions that a randomly selected student in the class answered correctly. The mean and standard deviation of X are 7.6 and 1.32 respectively. To determine each student's grade on the quiz, Ms. Newell will multiply his or her number of correct answers by 10. Let RV G be the grade of a randomly chosen student in the class.

Find the mean and standard deviation of G. Show your work

How are the mean and variance of G and X related?

If Johnny was simply guessing, what is the probability that he would pass?

Question#2

David's firm is planning a major investment. The amount of gross profit, indicated by RV 'X' (in millions of dollars) is uncertain, but an estimate gives the following empirical probability distribution:

Profit             1    1.5    2    4    10

Probability    0.1    0.2    0.4    0.2    0.1     

David's firm owes its venture capital lender a fee of 0.2 millions plus 10% of the gross profit X.  The retained profit is for David's firm is the RV 'Y'.

i. Calculate the mean and standard deviation of the gross profit.

Calculate the coefficient of variation of the gross profit.

Calculate the mean and standard deviation of the retained profit.

Calculate the coefficient of variation of the retained profit.

Question#3

Kobe Bryant, a former professional basketball player in the NBA, had made 84% of his free throws during his career with the Los Angeles Lakers.

a. Calculate the probability that Bryant would have made exactly three of his next five free throws.

b. Calculate the probability that Bryant would have made less than five of his next six free throws.

c. Calculate the probability that Bryant would have made four or five of his next six free throws.

Question#4

The city of Vancouver Office of Emergency Management reported that in a given time period, '911' operators receive an average of 7.2 calls per hour. Assume that the number of '911' calls follows Poisson distribution. 

a. What is the probability that exactly five '911' calls will be made during the next hour?

b. What is the probability that three or four '911' calls will be made during the next hour?

c. What is the probability that three or more '911' calls will be made during the next hour?

d. What is the probability that exactly four '911' calls will be made during the next 30 minutes?