Approximately normally distributed with a mean of 53.8 in, and standard deviation of 2.1 in. What is the probability that the height of a randomly chosen child is between 52.55 and 54.25 in?

Answer 1

want to find P(52.55 < x < 54.24) where x is height of randomly chosen child: x in normally distributed mean = 53.8 and standard deviation (SD) = 2.1

change limits of range so about standardized normal variable z (mean 0 SD = 1) instead of x where z = (x - mean)/SD = (x - 53.8)/2.1

P(52.55 < x < 54.25) =

P( (52.55 - 53.8)/2.1 < z < (54.25 - 53.8)/2.1) =

P(-0.6 < z < 0.21) =

P(z < 0.21) - P(z < -0.6) =

0.5832 - 0.2743 = 0.3089