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 37 gas stations is drawn from this population. What is the probability that the mean price for the sample was between ​$2.691 and ​$2.727 that​ week? Assume sigmaequals​$0.05.The probability that the sample mean was between ​$2.691 and ​$2.727 is ____

Answer 1

solution:-

given that mean = 2.704 , standard deviation sigma = 0.05 , n = 37

formula for z score = (x-mean)/(standard deviation/sqrt(n))

=> P(2.691 < X < 2.727) = P((2.691-2.704)/(0.05/sqrt(37)) < z < (2.727-2.704)/(0.05/sqrt(37)))

= P(-1.5815 < z < 2.7981)

= P(z < 2.7981) - P(z < -1.5815)

= P(z < 2.7981) - (1-P(Z < 1.5815))

= 0.9974 - (1-0.9429)

= 0.9974 - 0.0571

= 0.9403

note:-

z values from z standard normal distribution table