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Calculating mean, standard deviation and z-score

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Please help with the following statistics problem. Provide step by step calculations for each.

You learned that 27% of all small business owned by non-Hispanic whites nationwide are women-owned firms. In a random sample of 350 small businesses owned by non-Hispanic whites, let x be the number that are owned by a woman.

a) Find the mean of x.

b) Find the standard deviation of x.

c) Find the z-score for the value x= 99.5.

d) Find the approximate probability that the number of small businesses in the sample of 350 that are owned by a woman is 100 or more.

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Solution Summary

The following posting helps with calculations involving hypothesis testing. This solution describes the steps to find out mean, standard deviation and z-score in the given case. Step by step calculations are given for each problem.

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a) Find the mean of x.

p=probability that small business owned by non-hispanic whiles is woman=0.27
n=350
Mean=np=350*.27=94.5

b) Find the standard deviation of x.
Variance=np(1-p)=350*0.27*(1-0.27)= ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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