Question

According to an automobile​ association, the average cost of a gallon of regular unleaded fuel at gas stations in a certain month was

​$2.8282.828.

Assume that the standard deviation of such costs is

​$0.150.15.

Suppose that a random sample of

nequals=100

gas stations is selected from the population and the​ month's cost per gallon of regular unleaded fuel is determined for each. Consider

x overbarx​,

the sample mean cost per gallon. Complete part a through

d.

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Click the icon to view the table of normal curve areas.

a. Calculate

mu Subscript x overbarμx

and

sigma Subscript x overbarσx.

mu Subscript x overbarμxequals=nothing

​(Do not include the​ $ symbol in your answer. Round to three decimal places as​ needed.)

sigma Subscript x overbarσxequals=nothing

​(Do not include the​ $ symbol in your answer. Round to three decimal places as​ needed.)

b. What is the approximate probability that the sample has a mean fuel cost between​ $2.84 and​ $2.86?

​P(2.84less than or equals≤x overbarxless than or equals≤​2.86)equals=nothing

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

c. What is the approximate probability that the sample has a mean fuel cost that exceeds​ $2.855?

​P(x overbarxgreater than or equals≥​2.855)equals=nothing

d. How would the sampling distribution of

x overbarx

change if the sample size n were doubled from 100 to​ 200? Choose the correct answer below.

A.

mu Subscript x overbarμx

​doesn't change,

sigma Subscript x overbarσx

increases by a factor of 2

B.

mu Subscript x overbarμx

decreases by a factor of

StartRoot 2 EndRoot2​,

sigma Subscript x overbarσx

​doesn't change

C.

mu Subscript x overbarμx

​doesn't change,

sigma Subscript x overbarσx

decreases by a factor of 2

D.

mu Subscript x overbarμx

​doesn't change,

sigma Subscript x overbarσx

decreases by a factor of StartRoot 2 EndRoot2

How do your answers to parts b and c change when the sample size is​ doubled? Choose the correct answer below.

A.

​P(2.84less than or equals≤x overbarxless than or equals≤​2.86)

​increases,

​P(x overbarxgreater than or equals≥​2.855)

decreases

B.

​P(2.84less than or equals≤x overbarxless than or equals≤​2.86)

​decreases,

​P(x overbarxgreater than or equals≥​2.855)

increases

C.

​P(2.84less than or equals≤x overbarxless than or equals≤​2.86)

​decreases,

​P(x overbarxgreater than or equals≥​2.855)

decreases

D.

​P(2.84less than or equals≤x overbarxless than or equals≤​2.86)

​increases,

​P(x overbarxgreater than or equals≥​2.855)

increases

Answer 1