Question

A study found that highway drivers in one state traveled at an average speed of 54.1 miles per hour​ (MPH). Assume the population standard deviation is 5.4 MPH. Complete parts a through d below.

a. What is the probability that a sample of 30 of the drivers will have a sample mean less than 53 ​MPH?

P(x<53)=

​(Round to four decimal places as​ needed.)

b. What is the probability that a sample of 40 of the drivers will have a sample mean less than 53 ​MPH?

P(x<53)=

​(Round to four decimal places as​ needed.)

c. What is the probability that a sample of 50 of the drivers will have a sample mean less than 53​MPH?

P(x<53)=

​(Round to four decimal places as​ needed.)

d. Explain the difference in these probabilities.

As the sample size​ increases, the standard error of the mean

▼

decreases

stays the same

increases

and the sample means

▼

tend to move closer to

tend to move farther away from

stay about the same as

the population mean of

54.1

MPH.​ Therefore, the probability of observing a sample mean less than 53 MPH

▼

stays the same.

increases.

decreases.

Answer 1