Question

The random variable X is normally distributed. Also, it is known that P(X > 150) = 0.10. [You may find it useful to reference the z table.] a. Find the population mean μ if the population standard deviation σ = 15. (Round "z" value to 3 decimal places and final answer to 2 decimal places.) b. Find the population mean μ if the population standard deviation σ = 25. (Round "z" value to 3 decimal places and final answer to 2 decimal places.)

Answer 1

Answer)

A) Z = (X- mean) / (standard deviation)

Here standard deviation is = 15

and X = 150

z = 1.280 (from z table 1.28 = 0.8997 and 1-0.8997 = 0.1003(closest to 0.10) as p(z>x) = 1-p(z<x))

Therefore, 1.280 = (150-mean)/15

mean = 150 - 15*1.280

= 130.80

b) Here standard deviation is 25

therefore, 1.280 = (150-mean)/25

mean = 118.00