The fuel consumption, in miles per gallon, of all cars of a particular model has

Question

The fuel consumption, in miles per gallon, of all cars of a particular model has a mean of 29 and a standard deviation of 3. The population distribution can be assumed to be normal. A random sample of these cars is taken. Complete parts a and b below. a. Find the probability that the sample mean fuel consumption will be fewer than 28 miles per gallon if samples of 1, 4, and 9 are taken. The probability for a sample of 1 observation is (Round to four decimal places as needed.) b. Explain why the three answers in part (a) differ in the way they do. Draw a graph to illustrate your reasoning. As the sample size increases, the mean of the sampling distribution of X bar and the standard deviation Therefore, the sample means tend to the population mean, the portion of the sampling distribution of X bar that represents sample means fewer than 26 as the sample size increases. Which graph shows the correct relationship between the sampling distributions of X bar for two samples of n_1 and n_2 observations, where n_2 is larger than n_1 and x bar is a sample mean less than the population mean?

Explanation / Answer

a) P(X<28)=P(Z<(28-29)/3) =P(Z<-0.333)=0.3694

b)

the mean of the sampling distribution of X bar equal to population mean and the std deviation decreases. therefore ,,,,,,,tend to equal to population mean ..........fewer then 26 decreases as sample size increases.

for graph:

option C is correct.

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