1, The assets (in billions of dollars) of the four wealthiest people in a particular country are

31,29,24,18.

Assume that samples of size

n=2

are randomly selected with replacement from this population of four values.

Question content area bottom

Part 1

a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distribution of the sample mean. In the table, values of the sample mean that are the same have been combined.

x	Probability		x	Probability
31	enter your response here		24.5	enter your response here
30	enter your response here		24	enter your response here
29	enter your response here		23.5	enter your response here
27.5	enter your response here		21	enter your response here
26.5	enter your response here		18	enter your response here

(Type integers or fractions.)

2, The overhead reach distances of adult females are normally distributed with a mean of

195cm

and a standard deviation of

8.6cm.

a. Find the probability that an individual distance is greater than

208.40

cm.

b. Find the probability that the mean for

25

randomly selected distances is greater than 193.50cm.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Question content area bottom

Part 1

a. The probability is

enter your response here.

3, A boat capsized and sank in a lake. Based on an assumption of a mean weight of

144

lb, the boat was rated to carry

70

passengers (so the load limit was

10,080

lb). After the boat sank, the assumed mean weight for similar boats was changed from

144

lb to

171

lb. Complete parts a and b below.

Question content area bottom

Part 1

a. Assume that a similar boat is loaded with

70

passengers, and assume that the weights of people are normally distributed with a mean of

177.4

lb and a standard deviation of

37.7

lb. Find the probability that the boat is overloaded because the

70

passengers have a mean weight greater than

144

lb.

The probability is

enter your response here.