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Edit View History Bookmarks Window Help rmathxi.com StatisticsON2017 Homework: practice problems- module 10 Score: 0 of 1 pt HW Score: 2 (x 6.5.5 Ques Assume that women's heights are normally distributed with a mean given by u 64.3 in, and a standard deviation given by a -2.9 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 65 in. (b) 39 women are randomly selected, find the probability that they have a mean height less than 65 in. (a) The probability is approximately (Round to four decimal places as needed.) Dues the vari the vari my news

Explanation / Answer

Question 6.5.5

Part a

We are given µ = 64.3 and = 2.9

Here, we have to find P(X<65)

Z = (X - µ) /

Z = (65 – 64.3) / 2.9

Z = 0.241379

P(X<65) = P(Z< 0.241379) = 0.595369

Required probability = 0.595369

(By using excel or z-table)

Part b

We are given n = 39, µ = 64.3 and = 2.9

We have to find P(Xbar < 65)

Z = (X - µ)/ [/sqrt(n)]

Z = (65 – 64.3)/[2.9/sqrt(39)]

Z = 1.507413

P(Xbar<65) = P(Z< 1.507413) = 0.934148

Required probability = 0.934148

(By using excel or z-table)

Problem 6.5.11

We are given µ = 164, = 31

We have to find P(X>154)

P(X>154) = 1 – P(X<154)

Z = (X - µ) /

Z = (154 – 164)/31 = -0.32258

P(X<154) = P(Z<-0.32258) = 0.373506

P(X>154) = 1 - 0.373506 = 0.626494

Required probability = 0.626494

Problem 6.6.5

Correct answer: C. The distribution is not normal. The points are not reasonable close to a straight line.

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