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 60 and 64 inches? (c) If the tallest 15 % of the class is considered "very tall", what is the height cutoff for "very tall"? (d) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What percent of 10 year olds cannot go on this ride? %

Explanation / Answer

Part-a

P(X<48)= 0.1217 using excel function =NORMDIST(48,55,6,TRUE)

Part-b

P(60<X<64)= 0.1355 using excel function

= NORMDIST(64,55,6,TRUE)-NORMDIST(60,55,6,TRUE)

Part-c

Highest height= 61.22

Using excel function=NORMINV(0.85,55,6)

Part-d

Cannot go on ride=100*P(X<54)= 43.38 %

Using excel function=100*NORMDIST(54,55,6,TRUE)

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