Question

1. 4.3.5 Refer to Exercise 4.3.4. Find the mean and variance of the number of people tested for HIV in samples of size 15.
2. 4.3.6 Refer to Exercise 4.3.4. Suppose that we were to take a simple random sample of 25 adults today and find that two have been tested for HIV at some point in their life. Would these results be surprising? Why or why not? BINOMIAL TABLES
3. 4.3.7 Coughlin et al. (A-6) estimated the percentage of women living in border counties along the southern United States with Mexico (designated counties in California, Arizona, New Mexico, and Texas) who have less than a high school education to be 18.7. Assume the corresponding probability is .19. Suppose that we select three women at random. Find the probability that the number with less than a high-school education is: FORMULA FROM 4.3.2
   1. Exactly zero
   2. Exactly one
   3. More than one
   4. Two or fewer
   5. Two or three
   6. Exactly three

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1. 4.4.3 If the mean number of serious accidents per year in a large factory (where the number of employees remains constant) is five, find the probability that in the current year there will be:
   1. Exactly seven accidents
   2. Ten or more accidents
   3. No accidents
   4. Fewer than five accidents
2. 4.4.4 In a study of the effectiveness of an insecticide against a certain insect, a large area of land was sprayed. Later the area was examined for live insects by randomly selecting squares and counting the number of live insects per square. Past experience has shown the average number of live insects per square after spraying to be .5. If the number of live insects per square follows a Poisson distribution, find the probability that a selected square will contain:
   1. Exactly one live insect
   2. No live insects
   3. Exactly four live insects
   4. One or more live insects

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1. 4.6.3 P(z ≥ .55)
2. 4.6.4 P(z ≥ −.55)
3. 4.6.5 P(z < −2.33)
4. 4.6.6 P(z < 2.33)
5. 4.6.7 P(− 1.96 ≤ z ≤ 1.96)
6. 4.6.8 P(− 2.58 ≤ z ≤ 2.58)
7. 4.6.10 P(− 2.67 ≤ z ≤ z₁) = .9718
8. 4.6.11 P(z > z₁) = .0384

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1. 4.7.4 Suppose the average length of stay in a chronic disease hospital of a certain type of patient is 60 days with a standard deviation of 15. If it is reasonable to assume an approximately normal distribution of lengths of stay, find the probability that a randomly selected patient from this group will have a length of stay:
   1. Greater than 50 days
   2. Less than 30 days
   3. Between 30 and 60 days
   4. Greater than 90 days
2. 4.7.5 If the total cholesterol values for a certain population are approximately normally distributed with a mean of 200 mg/100 ml and a standard deviation of 20 mg/100 ml, find the probability that an individual picked at random from this population will have a cholesterol value:
   1. Between 180 and 200 mg/100 ml
   2. Greater than 225 mg/100 ml
   3. Less than 150 mg/100 ml
   4. Between 190 and 210 mg/100 ml

Answer 1

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