   Chapter 8.4, Problem 33E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Growth The heights of a certain species of plant are normally distributed, with mean μ = 20 cm and standard deviation σ = 4 cm. What is the probability that a plant chosen at random will be between 10 and 30 cm tall?

To determine

To calculate: The probability that a plant chosen at random will be between 10 and 30 cm using standard normal distribution if the heights of certain species of plant is normally distributed with μ=20 cm and σ=4 cm.

Explanation

Given Information:

A plant chosen at random will be between 10 and 30 cm, so the probability will be Pr(10x30).

The mean is μ=20 cm and the standard deviation σ=4 cm.

Formula used:

If data for a population are normally distributed, the z score is,

z=xμσ

Where σ is the standard deviation of the population data, x is the number of standard deviation and μ is mean.

Calculation:

Consider the provided probability Pr(10x30),

The mean is μ=20 cm and the standard deviation σ=4 cm.

To find the value of provided probability use the formula z=xμσ.

So this will convert into:

Pr(10204xμσ30204)=Pr(104z104)=Pr(2

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