Question

1. In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. It is known that 76% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 63 new products, find the following probabilities. (Round your answers to four decimal places.)

(a) within 2 years 47 or more fail

(b) within 2 years 58 or fewer fail

(c) within 2 years 15 or more succeed

(d) within 2 years fewer than 10 succeed

2. Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6950 and estimated standard deviation σ = 3000. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

3. Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 3 inches.

(a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? (Round your answer to four decimal places.)

(b) If a random sample of seven 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Round your answer to four decimal places.)

4. Suppose x has a distribution with μ = 27 and σ = 20.

(a) If a random sample of size n = 39 is drawn, find μ_x, σ_x and P(27 ≤ x ≤ 29). (Round σ_x to two decimal places and the probability to four decimal places.)

P(27 ≤ x ≤ 29) =

(b) If a random sample of size n = 65 is drawn, find μ_x, σ_x and P(27 ≤ x ≤ 29). (Round σ_x to two decimal places and the probability to four decimal places.)

P(27 ≤ x ≤ 29) =

Answer 1