Researchers wondered what the average braking distance is for new cars traveling
ID: 3296320 • Letter: R
Question
Researchers wondered what the average braking distance is for new cars traveling at 60 MPH. They randomly sampled 40 new cars made by two different companies. For each car, the same driver obtained a speed of 60 MPH and then pushed on the brake pedal as hard as she could. The average stopping distance for these 40 cars was 155.2 feet. Suppose
sigma
is known to be 12 feet. Assume that braking distances of the cars is independent. Are the other conditions satisfied to use the one-sample z-methods to construct a confidence interval?
Choose the correct answer below.
A.
No. The distribution of sample means will not be normal since the problem doesn't state that the braking distances of all new cars is normally distributed.
B.
No. Even though the distribution of sample means will be approximately normal because of the large samplesize, this sample of new cars is not representative of all new cars since a random sample of all new cars was not taken.
C.
Yes. The sample is representative of the population since a random sample was taken and the distribution of braking distances for all new cars will be normal since the sample size is more than 30.
D.
Yes. The sample is representative of the population since a random sample was taken and the distribution of sample means will be approximately normal since the sample size is more than 30.
Explanation / Answer
The sample is representative of the population since a random sample was taken and the distribution of sample means will be approximately normal since the sample size is more than 30. Also the population standard deviation is known therefore one sample z-test will be used. Note that here we are not studying the sample mean but finding the mean stoppage distance for the cars.
Therefore C is the correct answer here.
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