Question

1. The average price of a gallon of unleaded regular gasoline was reported to be $3.44 in northern Kentucky. Use this price as the population mean, and assume the population standard deviation is $0.30.
   1. What is the probability that the mean price for a sample of 50 service stations is within ±$.06 of the population mean?
   2. What is the probability that the mean price for a sample of 100 service stations is within ±$.06 of the population mean?

IN EXCEL

Answer 1

Answer:

(a)

We know that,

Given, X-u=0.06

n=50 and sigma=0.30

Thus, Z=0.06/(0.3/7.07)=0.06/0.0424=1.415

Hence, P(Z≤1.415)=0.92073

(b) Here,

X-u=0.06

n=100 and sigma=0.30

Thus, Z=0.06/(0.3/10)=0.06/0.03=2

Hence, P(Z≤2)=0.97725

Thus, the probability that the mean price for a sample of 50 service stations is within ±$.06 of the population mean is 0.92073 and the probability that the mean price for a sample of 100 service stations is within ±$.06 of the population mean is 0.97725.