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

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Most normal : Figure at bottom right. Since n is the highest it tends to be more normal.

Least normal: Figure at top left. Since it has the least sample size.

Yes, np for last figure is .1*100 = 10

n(1-p) for last figure is 100*(1-.1) = 90

For approximate normality we must have both figures atleast 10.

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