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 28 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. Click on the icon to view the standard normal table. a. Find the probability that the sample mean fuel consumption will be fewer than 27 miles per gallon if samples of 1, 4, and 9 are takern The probability for a sample of 1 observation is (Round to four decimal places as needed.) The probability for a sample of 4 observations is Round to four decimal places as needed.) The probability for a sample of 9 observations 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 I and the standard deviation | Therefore, the sample | the population mean. Since 27 is less than the means tend to population mean, the portion of the sampling distribution of X that represents sample means fewer than 27 | as the sample size increases. Click to select your answer(s). Save for Later

Explanation / Answer

Ans:

mean=28,standard deviation=3

a)when n=1

z=(27-28)/3=-0.33

P(z<-0.33)=0.3694

when n=4

standard deviation=3/sqrt(4)=1.5

z=(27-28)/1.5=-0.67

P(z<-0.67)=0.2525

when n=9

standard deviation=3/sqrt(9)=1

z=(27-28)/1=-1

P(z<-1)=0.1587

b)mean remains same and standard deviation decreases.

therefore,the sample means tend to be farther/away from the population mean.Since 27 is less than the population mean,the portion of sampling distribution of sample means that represent sample means fewer than 27 decreases(from 0.3694 to 0.1587),as the sample size increases

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