Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

The American Auto Association reports the mean price per gallon of regular gasol

ID: 3207564 • Letter: T

Question

The American Auto Association reports the mean price per gallon of regular
gasoline is $4.10 with a population standard deviation of $0.70. Assume a
random sample of 25 gasoline stations is selected and their mean cost for
regular gasoline is computed.


a. Determine the standard error of the mean
b. What is the probability that the sample mean is between $3.98 and
$4.12?
c. What is the probability that the difference between the sample mean
and the population mean is less than 0.01?
d. What is the likelihood the sample mean is greater than $4.08?
e. What is the likelihood the sample mean is less than 4.13?

Show All Work

Explanation / Answer

(a) SE = /n = 0.70/25 = 0.14

(b) z1 = (3.98 - 4.10)/0.14 = -0.8571 and z2 = (4.12 - 4.10)/0.14 = 0.1429

P(3.98 < x-bar < 4.12) = P(-0.8571 < z < 0.1429) = 0.3611

(c) z = 0.01/0.14 = 0.0714

P[(x - ) < 0.01] = P(z < 0.0714) = 0.5285

(d) z = (4.08 - 4.10)/0.14 = -0.1429

P(x-bar > 4.08) = P(z > -0.1429) = 0.5568

(e) z = (4.13 - 4.10)/0.14 = 0.2143

P(x-bar < 4.13) = P(z < 0.2143) = 0.5848.