Let x represent the dollar amount spent on supermarket impulse buying in a 10-mi

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 $19 and the estimated standard deviation is about $5.

(a) What is the probability that x is between $17 and $21? (Round your answer to four decimal places.)

(b) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $17 and $21? (Round your answer to four decimal places.)

Explanation / Answer

n =10 , s = 5 , mean = 19

P(17 < x < 21)

z = ( x -mean) / ( s/sqrt(n))

P(x<17)

z = ( 17 - 19) / ( 5 / sqrt(10))

= -1.264

P(x < 21)

z = ( 21 - 19) / ( 5/sqrt(10))

= 1.264

P(17 < x <21) = P(-1.264 < z < 1.264) = 0.7944

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