It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conducts diagnostic tests on 128 new cars on the lot.
a. Describe the sampling distribution for the sample proportion by naming the model and telling its mean and standard deviation.
b. What is the probability that in this group over 18% of the new cars will be found to have electrical problems?

Question

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The Answer is a. We can assume these cars are a representative sample of all new cars, and certainly less than 10% of them. We expect 14% × 128 = 17.92 successes (electrical problems) and 86% × 128 = 110.08 failures (no problems) so the sample is large enough to use the sampling model N(0.14, 0.031).
b. z =

a. We can assume these cars are a representative sample of all new cars, and certainly less than 10% of them. We expect 14% × 128 = 17.92 successes (electrical problems) and 86% × 128 = 110.08 failures (no problems) so the sample is large enough to use the sampling model N(0.14, 0.031). b. z = = 1.29, about 10%

= 1.29, about 10%

It Is Generally Believed That Electrical Problems Affect About 14