Determinations of the ultimate tensile strength S of stainless-steel sheet (17–7PH, condition TH 1050), in sizes from 0.016 to 0.062 in, in 197 tests combined into seven classes were S„(kpsi) 174 206 214 222 53 182 190 198 6 9 44 67 12 6 where S is the class midpoint and f is the class frequency. Estimate the mean and standard deviation. Plot the histogram and the corresponding normal distribution. Discuss how well uniform PDF describes this histogram.

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Determinations of the ultimate tensile strength S of stainless-steel sheet (17–7PH, condition TH 1050), in sizes
from 0.016 to 0.062 in, in 197 tests combined into seven classes were
S„ (kpsi)
182
44
190 198
67
206 214 222
12
174
6
9
53
where S, is the class midpoint and f is the class frequency. Estimate the mean and standard deviation. Plot the
histogram and the corresponding normal distribution. Discuss how well uniform PDF describes this histogram.
Transcribed Image Text:Determinations of the ultimate tensile strength S of stainless-steel sheet (17–7PH, condition TH 1050), in sizes from 0.016 to 0.062 in, in 197 tests combined into seven classes were S„ (kpsi) 182 44 190 198 67 206 214 222 12 174 6 9 53 where S, is the class midpoint and f is the class frequency. Estimate the mean and standard deviation. Plot the histogram and the corresponding normal distribution. Discuss how well uniform PDF describes this histogram.
Expert Solution
Step 1

Using Excel to compute the required values as follows:

  • Input data in excel column-wise
  • To Calculate mean of the given data using formula:

Mean=1Nifixi   where N=ifi

Compute the following column:

Probability homework question answer, step 1, image 1

  • Use command:

Probability homework question answer, step 1, image 2

This gives the value of mean = 198.6091

  • Similarly, for standard deviation, the formula is:

SD=1Nifixi-Mean2

Compute further the columns:

Probability homework question answer, step 1, image 3

  • Use command:

Probability homework question answer, step 1, image 4

This gives value of SD = 9.67043

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