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 $2.704 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

Answer 1

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