Heights of 10 year olds, regardless of gender, closely follow a normal distribut

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? b) What is the probability that a randomly chosen 10 year old is between 48 and 54 inches? c) The minimum height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What percent of 10 year olds can go on this ride? d) If the tallest 10% of the class is considered "very tall, " what is the height cutoff for "very tall"?

Explanation / Answer

Params of normal distributions are given:

Mean = 55

Stdev = 6

a. P(X<48) = P(X< 48-55 / 6) = P(Z< -1.167) = .1230

b. P(48<X<54) = P(-1.167<Z<.167) = .4364-.1230 = .3134

c. P(X>54) = ?, P(Z> 54-55/6) = .1230

d. P(X>a) = .10, a=?, Look at Z tables the top 10% is Z=1.28 on the Z tables.
So, a = 1.28*6+55 = 62.68

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