The time (in seconds) to complete a task is recorded for three elderly subjects.The results are:

10302020 2020

a)What is the sample mean?

b)What is the sample standard deviation?

5.Fifty randomly chosen people are cross-classified by sex and whether they are HIV positive or HIV negative.The results are in the table below.

Female

Male

HIV Positive

4

16

HIV Negative

14

16

a)If one person is chosen at random from these 25, find the following probabilities.

i.P( FemaleandHIV Positive )

ii.P( HIV Positive|Female )

iii.P( HIV Positive|Male )

b)Are sex and HIV status independent?Make sure to justify your answer.

c)Suppose we select 3 people, without replacement, at random from these 50 people.Find the probability that they are both HIV positive.