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Question

Find the probability and interpret the results. If convenient, use technology to find the probability. During a certain week the mean price of gasoline was $2.713

per gallon. A random sample of 32

gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.695

and $2.724

that week? Assume sigma
equals $0.042.

The probability that the sample mean was between $2.695

and $2.724

is?
.
(Round to four decimal places as needed.)

Answer 1

Use Z scores:    z_upper = (2.724 - 2.713) / σ and z_lower = (2.695 - 2.713) / σ.

 

Then the probability of prices between the upper and lower prices-per-gallon is computed by looking up the areas under the standard normal distribution curve, and taking their difference.