x = x = What is the approximate probability that the sample has a mean fuel cost
ID: 3177637 • Letter: X
Question
x =x =
What is the approximate probability that the sample has a mean fuel cost between 2.84and 2.86
What is the approximate probability that the sample has a mean fuel cost that exceeds 2.885
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What is the approximate probability that the sample has a mean fuel cost between 2.84and 2.86
What is the approximate probability that the sample has a mean fuel cost that exceeds 2.885
w History Bookmarks People Window Help Bonnie Clark Secure https:llwwwmathod.comist udentPlayerHomework aspx?homeworkid-42 3&t; 4223703258questionld 42747758 center 315/17 1236 PM Spring 2017 STAT 211-016 (TR 150 PM Bonnie Clark Homework: HW #7: Chapter 15 5 of 7 (6 complete) v Score: 0.67 of 2 pts HW Score: 76.67%, 7.67 of 10 pts EQuestion Hep 6.3.42 Aooording to an automobile associaton.the average cost of a galon ofreguar unleaded fuel at gas stasons in a certain month was s2.826 Assume that the standard deviation of such costs is 15 suppose that a random sample of n. 100 gas stations is selected from the population and the month's cost per galon of regular unleaded fuel is determined for each Consider x the sample mean oost per galon Complete part athrough d con to view the table of normal curve areas. Do not ndude thessn bolin your answer. Round to tree decimal places as needed tema ing
Explanation / Answer
Here mean=2.826 and sd=0.15
As n=100, as per central limit theorem sampling distribution will have mean of mu=xbar=2.826 and sd=sd/sqrt(n)=0.15/10=0.015
Now we need to find P(2.84<xbar<2.86)=P(2.84-2.826/0.015<z<2.86-2.826/0.015)=P(0.93<z<2.267)=P(0<z<2.267)-P(0<z<0.93)=0.4883-0.3238=0.1645
P(xbar>2.885)=P(z>3.93)=0.5-P(0<=z<=3.93)=0.5-0.5=0
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