(Q24-Q25) Suppose the mean selling price of a gallon of gasoline in Sacramento i

Question

(Q24-Q25) Suppose the mean selling price of a gallon of gasoline in Sacramento is $3.70. Further, assume the population distribution is highly positively skewed, with a population standard deviation of $0.60. A sample of 36 gasoline stations is chosen. Then, most (99.7%) of sample means should range between _______and____values. Show your solution

A.) $3.20 and $4.20

B.) $3.40 and $4.00

C.) $3.50 and $3.90

D.) $3.60 and $3.80

E.) $3.00 and $4.40

Q25: What is the probability of finding the sample mean within $.20 of the population mean? Show your solution.

A.) 50%

B.)68%

C.) 86%

D.) 95%

E.) 99.7%

Explanation / Answer

Confidence interval = mean +/- Z* SD/sqrt(n)

= 3.7 +/- 2.97 * 0.6/sqrt(36)

= 3.7 +/- 0.297

= 3.403, 3.997

= 3.40, 4

Option-B is the correct answer.

B) margin of error = Z * SD/sqrt(n)

Or, 0.2 = Z * 0.6/6

Or, Z = 2

P(Z < 2) = 0.9772

Probability = 1 - 2 *(1 - 0.9772)

= 0.9544 = 95.44% = 95

Option-D is the correct answer.

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