The number of boxes of girl scout cookies sold by each of thegirl scouts in a mi

Question

The number of boxes of girl scout cookies sold by each of thegirl scouts in a mid-western city has a distribution which is approximatelynormal with mean, m = 75 boxes and standard deviation, s = 30 boxes. a. Find the probability that a scout chosen at randomsold between 60 and 90 boxes of cookies. b. Find the probability that the sample mean number ofboxes of cookies sold by a random sample of 36 scouts is between 60 and 90boxes. c. What difference do you observe in the two answers?Explain.
The number of boxes of girl scout cookies sold by each of thegirl scouts in a mid-western city has a distribution which is approximatelynormal with mean, m = 75 boxes and standard deviation, s = 30 boxes. a. Find the probability that a scout chosen at randomsold between 60 and 90 boxes of cookies. b. Find the probability that the sample mean number ofboxes of cookies sold by a random sample of 36 scouts is between 60 and 90boxes. c. What difference do you observe in the two answers?Explain.

Explanation / Answer

a. Find the probability that a scout chosen at randomsold between 60 and 90 boxes of cookies.

P(60<X<90)= P((60-75)/30<(X-)/ < (90-75)/30)
=P(-0.5<Z<0.5)
=0.3829 (check normal table)

b. Find the probability that the sample mean number ofboxes of cookies sold by a random sample of 36 scouts is between 60 and 90 boxes.

P(60<Xbar<90)= P((60-75)/(30/sqrt(36))<(Xbar-)/(/n)< (90-75)/(30/sqrt(36)))
=P(-3<Z<3)
=0.9973 (checknormal table)

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