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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 taller than 48 inches? .878 b) What is the probability that a randomly chosen 10 year old is between 60 and 65 inches? .155 c) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What proportion of 10 year olds cannot go on this ride?

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 taller than 48 inches? .878 b) What is the probability that a randomly chosen 10 year old is between 60 and 65 inches? .155 c) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What proportion of 10 year olds cannot go on this ride?

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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I need help figuiring out C the proportion part of this.

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 taller than 48 inches? .878 b) What is the probability that a randomly chosen 10 year old is between 60 and 65 inches? .155 c) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What proportion of 10 year olds cannot go on this ride?
Transcribed Image Text: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 taller than 48 inches? .878 b) What is the probability that a randomly chosen 10 year old is between 60 and 65 inches? .155 c) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What proportion of 10 year olds cannot go on this ride?
Expert Solution
Step 1

Given information:

The heights of 10-year-olds, regardless of gender, are normally distributed.

Population mean, μ=55 inches

Population standard deviation, σ=6 inches

If X represents the heights of 10-year-olds, then, it can be written as:

X~N55,6

It is required to obtain:

c) The proportion of 10-year-olds who cannot go on the ride if the height requirement for Batman the Ride at Six Flags Magic Mountain is X = 54 inches.

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