Question

Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. (a) what is the probability that a randomly chosen 10 year old is shorter than 48 inches? (please round to four decimal places)

Answer 1

Given:
μ = 55 in, population mean
σ = 6 in, population standard deviation

Part (a)
x = 48 in, the random variable
Calculate the z-score.
z = (x - μ)/σ
   = (48 - 55)/6
   = -1.667
From standard table, obtain
P(X < 48) = 0.12167 

Answer: 0.1217  (tyo 4 dec.places)