Chapter 7, Section 7.3, Question E43 The GMAC Insurance National Driver\'s Test

Question

Chapter 7, Section 7.3, Question E43 The GMAC Insurance National Driver's Test found that about 10% of drivers ages 16 to 65 would fail a written driver's test if they had to take one today. [Source: Insurance Journal, 2005, www.insurancejournal com. The sampling distributions in the figure below give the proportion of drivers who would fail for samples of sizes 10, 20, 40, and 100 taken from a population where p 0.10 0.40 0.30 0.20 0.10 0.00 0.30 0.20 0.10 0.00 0.2 0.6 1.0 Sampling Distribution for n = 10 and p 0.10 0.2 0.6 1.0 Sampling Distribution for n 20 and p 0.10 0.20 0.16 0.12 0.08 0.04 0.00 0.14 0.10 0.06 0.02 0.2 0.6 10 Sampling Distribution for n-40 and p 0.10 000.2040.60.81.0 Sampling Distribution for n 100 and p 0.10 Exact sampling distributions of p for samples of size 10, 20,40, and 100 whenp 0.10 Which distribution is most normal in space? Least normal? Does the guideline that both np and n(1-?) should be at least 10 work well in predicting approximate normality?

Explanation / Answer

Most normal: 4th sampling distribution, with n=100, p=0.10. Because the graph shows symmetricity and shape of a bell which are properties of a normal distribution.

Least Normal : 1st sampling distribution with n = 10, p=0.10, because it's skewness is ore than that of the other sampling distributions.

Yes, the guideline works well. Because we see that both np and n(1-p) are greater than 10 when n=100 (Most normal). and none of them are>10 when n=10(least normal).

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