Question

In: Statistics and Probability

Suppose in December 2019, the average and standard deviation of gas price at gas stations were...

Suppose in December 2019, the average and standard deviation of gas price at gas stations were 136.5 and 6 ¢/liter respectively. A random sample of n = 36 gas stations is selected from the population and the price per liter of gas is determined for each.

a) Describe the distribution of the average gas price determined for this sample gas stations. What are the values of mean and standard deviation for this distribution?

b) What is the probability that the mean gas price of the sample is between 135 ¢/liter and 138 ¢/liter?

c) Suppose we wish to estimate the average gas price within 0.9 ¢/liter of its true value with a 95% confidence interval. What sample size should be specified for the experiment? (σ ≈ 6)

Expert Solution

a)

According to the Central Limit Theorem, the distribution of the average gas price is Normal distribution.

mean = 136.5

standard deviation = 6 / = 1

b)

Probability that the mean gas price of the sample is between 135 ¢/liter and 138 ¢/liter

= P(135 < < 138)

= P( < 138) - P( < 135)

= P[Z < (138 - 136.5)/1] - P[Z < (135 - 136.5)/1]

= P[Z < 1.5] - P[Z < -1.5]

= 0.9332 - 0.0668

= 0.8664

c)

Margin of error, E = 0.9 ¢/liter

Standard deviation, = 6

Z score for 95% confidence interval is 1.96

Sample size , n = = 170.7378

171 (Rounded to nearest integer)

orchestra answered 2 years ago

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