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 andstandard deviation 6 inches.a) What is the probability that a randomly chosen 10 year old is taller than 48 inches? .878b) What is the probability that a randomly chosen 10 year old is between 60 and 65 inches?.155c) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What proportion of10 year olds cannot go on this ride?

Answered: Heights of 10 year olds, regardless of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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?

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:

$X ~ N (55, 6)$

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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