If five measurements are taken at various times during the day, what is the probability

4.88 Use the binomial distribution with n ⫽ 20, p ⫽ .5 to compare accuracy of the normal approximation to the binomial.

a. Compute the exact probabilities and corresponding normal approximations for y

⬍ 5.

b. The normal approximation can be improved slightly by taking Py

ⱕ 4.5. Why should this help? Compare your results.

c. Compute the exact probabilities and corresponding normal approximations with the

continuity correction for P8 ⬍ y ⬍ 14.

4.89 Let y be a binomial random variable with n

⫽ 10 and p ⫽ .5.

a. Calculate P4

ⱕ y ⱕ 6.

b. Use a normal approximation without the continuity correction to calculate the

same probability. Compare your results. How well did the normal approximation work?

4.90 Refer to Exercise 4.89. Use the continuity correction to compute the probability P4

ⱕ y ⱕ 6. Does the continuity correction help? Bus. 4.91 A marketing research firm believes that approximately 12.5 of all persons mailed a sweepstakes offer will respond if a preliminary mailing of 10,000 is conducted in a fixed region. a. What is the probability that 1,000 or fewer will respond? b. What is the probability that 3,000 or more will respond? 4.14 Evaluating Whether or Not a Population Distribution Is Normal 4.92 In Figure 4.19, we visually inspected the relative frequency histogram for sample means based on two measurements and noted its bell shape. Another way to determine whether a set of measurements is bell-shaped normal is to construct a normal probability plot of the sample data. If the plotted points are nearly a straight line, we say the measurements were selected from a normal population. We can generate a normal probability plot using the following Minitab code. If the plotted points fall within the curved dotted lines, we consider the data to be a random sample from a normal distribution. Minitab code: 1. Enter the 45 measurements into C1 of the data spreadsheet. 2. Click on Graph, then Probability Plot.

3. Type c1 in the box labeled Variables. 4. Click on OK.

99 95 90 80 70 60 50 40 30 20 10 5 1 2 1 7 2 Percent ML Estimates Mean: 6.5 StDev: 1.91485