Find the probability and interpret the results. If convenient, use technology to find the probability. During...

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 $2.704 per gallon. A random sample of 38 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.683 and $2.722 that week? Assume o= $0.046

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Expert Solution

Solution :

Given that,

mean = = 2.704

standard deviation = = 0.046

n = 38

= = 2.704

= / n = 0.046 / 38 = 0.0075

P(2.683 < < 2.722) = P((2.683 - 2.704) / 0.0075 <( - ) / < (2.722 - 2.704) / 0.0075))

= P(-2.8 < Z < 2.4)

= P(Z < 2.4) - P(Z < -2.8) using z table,

= 0.9918 - 0.0026

= 0.9892

The probability that the mean price for the sample was between $2.683 and $2.722 that week is 0.9892

orchestra answered 1 year ago

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