All 10 automobiles failed the inspection. b. Exactly 6 of the 10 failed the inspection.

c. Use a normal approximation to compute the probability that less than six sales are made. d. Use a Poisson approximation to compute the probability that less than six sales are made.

e. Use a computer program if available to compute the exact probability that less than

six sales are made. Compare this result with your calculations in c and d. 4.52 A certain birth defect occurs in 1 of every 10,000 births. In the next 5,000 births at a major hospital, what is the probability that at least one baby will have the defect? What assumptions are required to calculate this probability? 4.10 A Continuous Probability Distribution: The Normal Distribution 4.53 Use Table 1 of the Appendix to find the area under the normal curve between these values:

a. z ⫽ 0 and z ⫽ 1.6 b. z ⫽ 0 and z ⫽ 2.3

4.54 Repeat Exercise 4.53 for these values: a. z ⫽ .7 and z ⫽ 1.7

b. z ⫽ ⫺1.2 and z ⫽ 0 4.55 Repeat Exercise 4.53 for these values:

a. z ⫽ ⫺1.29 and z ⫽ 0 b. z ⫽ ⫺.77 and z ⫽ 1.2

4.56 Repeat Exercise 4.53 for these values: a. z ⫽ ⫺1.35 and z ⫽ ⫺.21

b. z ⫽ ⫺.37 and z ⫽ ⫺1.20 4.57 Find the probability that z is greater than 1.75.

4.58 Find the probability that z is less than 1.14. 4.59 Find a value for z, say z

, such that Pz ⬎ z ⫽ .5.

4.60 Find a value for z, say z , such that Pz ⬎ z

⫽ .025.

4.61 Find a value for z, say z , such that Pz ⬎ z

⫽ .0089.

4.62 Find a value for z, say z , such that Pz ⬎ z

⫽ .05.

4.63 Find a value for z, say z , such that P⫺z

⬍ z ⬍ z ⫽ .95. 4.64 Let y be a normal random variable with mean equal to 100 and standard deviation equal to 8. Find the following probabilities:

a. Py ⬎ 100 b. Py ⬎ 105

c. Py ⬍ 110 d. P88 ⬍ y ⬍ 120

e. P100 ⬍ y ⬍ 108

4.65 Let y be a normal random variable with m ⫽ 500 and s ⫽ 100. Find the following proba- bilities:

a. P500 ⬍ y ⬍ 665 b. Py ⬎ 665

c. P304 ⬍ y ⬍ 665 d. k such that P500 ⫺ k ⬍ y ⬍ 500 ⫹ k ⫽ .60

4.66 Suppose that y is a normal random variable with m ⫽ 100 and s ⫽ 15. a. Show that y ⬍ 115 is equivalent to z ⬍ 1.

b. Convert y ⬎ 85 to the z-score equivalent. c. Find Py ⬍ 115 and Py ⬎ 85.

d. Find Py ⬎ 106, Py ⬍ 94, and P94 ⬍ y ⬍ 106. e. Find Py ⬍ 70, Py ⬎ 130, and P70 ⬍ y ⬍ 130.

4.67 Find the value of z for these areas. a. an area .025 to the right of z

b. an area .05 to the left of z