A population of values has a norm. distribution with a mean of 51.2 and standard dev. of 12.5. You want to draw a sample of size 112.

Question

Find the prob. that a single randomly selected value is between 51.1 & 51.8.

Answer 1

sample size (n) = 112

population mean = 51.2

population standard deviation 12.5

x = value, want to find P(51.1 < x < 51.8)

x is non-standard normally distributed N(51.2,12.5)

convert x = 51.1 and 51.8 to standard normally distributed N(0,1) via equation z = (x - population mean)/population standard deviation. z is N(0,1).

convert x = 51.1: (51.1-51.2)/12.5 = -0.008

convert x = 51.8: (51.8-51.2)/12.5 = 0.048

P(51.1 < x < 51.8) --> P(-0.008 < z < 0.048) = 0.0239