The random variable X is normally distributed. Also, it is known that P(X > 184)

Question

The random variable X is normally distributed. Also, it is known that P(X > 184) = 0.04. Use Table 1. a. Find the population mean , if the population standard deviation = 10. (Round "z" value to 2 decimal places and final answer to 1 decimal place.) Mean b. Find the population mean , if the population standard deviation = 18. (Round "z" value to 2 decimal places and final answer to 1 decimal place.) Mean c. Find the population standard deviation , if the population mean = 167. (Round “z” value to 2 decimal places, and final answer to 2 decimal places.) Standard deviation d. Find the population standard deviation , if the population mean = 152. (Round “z” value to 2 decimal places, and final answer to 2 decimal places.) Standard deviation

Explanation / Answer

P(X>184) = .04

a.

So, 184-Mean / 10 = 1.75

X = 184-17.5

X=166.5

b)

184-Mean / 18 = 1.75

Mean = 152.5

c)

184-167 / sigma = 1.75

Sigma = (17/1.75)

Sigma = 9.71

d)

184-152 / Sigma = 1.75

Sigma = 32/1.75 = 18.29

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