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According to the latest financial reports from a sporting goods store, the mean sales per customer...

According to the latest financial reports from a sporting goods store, the mean sales per customer was $75 with a population standard deviation of $6. The store manager believes 39 randomly selected customers spent more per transaction. What is the probability that the sample mean of sales per customer is between $76 and $77 dollars?

mean:

standard deviation:

P(76< X < 77)=

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that ,

mean = = $75

standard deviation = =$6

= / n = 6 / 39 = 0.9608

= P[(76 - 75) /0.9608 < ( - ) / < (77 - 75) / 0.9608)]

= P(1.04 < Z < 2.08)

= P(Z < 2.08) - P(Z < 1.04)

= 0.9812 - 0.8508

= 0.1304

P(76 < X < 77) = 0.1304

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