Question

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $40 and the estimated standard deviation is about $8. What is the probability that x is between $38 and $42? (Round your answer to four decimal places.) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $38 and $42? (Round your answer to four decimal places.)

Answer 1

Assuming, X ~ N(40, 8) approximately, Z = (X - 40)/8 ~ N(0,1)

We have, P(38 < X < 42) = P[(38 - 40)/8 < (X - 40)/8 < (42 - 40)/8] = P[-0.25 < (X - 40)/8 < 0.25] = (0.25) - (-0.25) = 0.5987 - 0.4013 = 0.1974

[(.) is the cdf of N(0,1)]

Hence, the probability of X is between 38 and 42 is 0.1974.