Short answers:

a. If the mode is smaller than mean for a data set, what can you conclude about the data's distribution?

b. Calculate the variance for a data set following Poisson distribution when the average rate of occurrence is 8.9 in an hour?

c.Suzanne is scored in the 81st percentile on the GRE. If 6,000 people took that test, how many people had a score at least as high as Suzanne?

2, Use the data that is given in the following Stem plot and answer questions "a" to "c

Stem Leaf

10 - 0 1 3 4 7

11 - 2 3 4 7 7

12- 3 8 8 8 8

13 -

14 - 0 4 4 4 4

a. Find the mode, mean and standard deviation for this data set

b. Find Q1 and Q3 and represent this data using a box plot

c. What is the 85th percentile?

3) 50% of students in a class are from Europe, 25% are from Asia and the rest are from South American countries. 55% of Europeans, 58% of Asians and 60% of South Americans are female. We have selected a female student. What is the chance that she is European?

4) The distribution of the time it takes a chef to cook the new order of a customer follows a normal distribution with the mean value of 35 minutes and standard deviation of 5 minutes.

a. What is the probability that it takes the Chef exactly 35 minutes to make a randomly selected customer's dish?

b. What is the chance that it takes the Chef any time between 15 and 35 minutes to cook the food?

c.What is the chance that it takes the Chef more than 45 minutes to make a dish for a customer?

5) An insurance company is selling insurance to men age 95 and above. The chance that a customer survives another year is 0.97. The premium costs $4160 per year and the insurance company pays $500,000 in case the customer does not survive.

a. Suppose that 10 people are insured. What is the chance that half of them survive?

b. What is the expected profit/loss of the company per customer?

6) 200 students of ages 14 to 18 in a certain height range are randomly selected for a study. Their weights follow the normal distribution with the minimum weight of 42 kg and the maximum weight of 78 kg.

a) What is the range for the mid 68% of the weights?

b) Doctors require to examine a weight loss exercise plan on kids whose weights are in the fourth quartile of the set. Find the minimum weight applicable to this weight loss plan.

c) How many kids will be subject to this weight loss plan?