Question 14 on A and Question 21 on B

In 2007, the percentage of people in Botswana expected to have the HIV virus was 23.9%. Assume that this percentage has not changed. Suppose that a researcher selects 5 people at random from the population of Botswana.

What is the expected number of people in the sample to have the HIV virus?

a.) 1

b.) 1.195

c.) 2

d.) 2.195

e.) Cannot be determined

The correct answer is B.

The mean is not required to be a whole number. When you get a decimal answer, the answer should be left as a decimal rather than round to a whole number. Rounding the value either inflates or deflates the real size of the mean.

In class on page 48 on the handbook, we found that the expected number of people that had side effects from the medication was mean = np=8*(0.35) =2.8. This means that not quite 3 people have side effects from the medication out of 8 people. The correct answer was 2.8.

This was also illustrated in one of the questions of the day.

“Suppose that a college level basketball player has an 80% chance of making a free throw. Suppose that he shoots 8 free throws in a game. What is his expected number of baskets? “ For this problem, the answer was 8*0.80 = 6.4.

Remember that this is not asking for just the number of people. This is asking for the expected number of people or the average number of people. The average should not be rounded to a whole number.

For example, if a town wants to build a new school, they figure that they have 10,000 families in their community with an average of 1.7 children per household. If they want to determine the number of children in the community, they would multiply 10000*1.7 = 17000. If they rounded the average up to 2, they would estimate that there were 10000*2 = 20000 children in the town. This is an overestimation of the number of children. The town might not adequately allocate resources in the town if they used the 20000 children value. Since they thought that they had so many children, money might be taken from senior care for example.

The best answer for this problem was 1.195.