Business Statistics (15.02) 2 Trans ools Help RAHMAN KAMARA Lesson 7.3c-z z-Tran

Question

Business Statistics (15.02) 2 Trans ools Help RAHMAN KAMARA Lesson 7.3c-z z-Transformations NESS on 2 of 10, Step 1 of ISTICS PROBLEM The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.57 millimeters and a standard deviation of 0.08 millimeters. Find the two diameters that separate the top 8% and the bottom 8%. These diameters could serve as limits used to identify boits should be rejected. Round your answer to the nearest hundredth, if necessary EARN ANSWE R ACTICE Enter your answer in the boxes below millimeters millimeters and Answer ERTIFY Standard Normal Table s to z Sandard Normal Table - to z

Explanation / Answer

here mean is 5.57

std deviation is 0.08 , we can use normal dstribution here,

we have to find the X such that P(X>x1) = 0.08 and P(X<x2) = 0.08

P(X>x1) = 0.08

or P(Z>(x1-5.57)/0.08) = 0.08

(x1-5.57)/0.08=1.41

x1 = 5.57+1.41*0.08 = 5.6828

similarly

P(X<x2) = 0.08

or P(X<(x2-5.57)/0.08) = 0.08

(x2-5.57)/0.08=-1.41

x2 = 5.57-1.41*0.08 = 5.4572

so the answers are 5.4572 and 5.6828

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