   # Botany In a botany experiment, plants are grown in a nutrient solution. The heights of the plants are found to be normally distributed with a mean of 42 centimeters and a standard deviation of 3 centimeters. (a) Use a graphing utility to graph the distribution. (b) Use a symbolic integration utility to approximate the probability that the height of a plant is between 40 and 45 centimeters. (c) Use a symbolic integration utility to approximate the probability that the height of a plant is less than 50 centimeters. ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 62RE
Textbook Problem
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## Botany In a botany experiment, plants are grown in a nutrient solution. The heights of the plants are found to be normally distributed with a mean of 42 centimeters and a standard deviation of 3 centimeters.(a) Use a graphing utility to graph the distribution.(b) Use a symbolic integration utility to approximate the probability that the height of a plant is between 40 and 45 centimeters.(c) Use a symbolic integration utility to approximate the probability that the height of a plant is less than 50 centimeters.

(a)

To determine

To graph: The sketch of distribution of the growth of plants in a nutrient solution using graphing utility where the scores are normally distributed with a mean and standard deviation of heights of the plants is 42 and 3 cm respectively.

### Explanation of Solution

Given Information:

The mean and standard deviation of heights of the plants is 42 and 3 cm respectively that are normally distributed.

Graph:

The normal probability density function is given by

f(x)=1σ2πe(xμ)2(2σ2),<x<

Substitute μ=42 and σ=3 in the above equation,

f(x)=132πe(x42)22(3)2=0.133e(x42)218

Now use Ti-83 calculator to draw the graph of the above function

(b)

To determine

To calculate: The approximate probability that the height of the plants is between 40 and 45 cm using symbolic integration utility.

(c)

To determine

To calculate: The approximate probability that the height of the plants is less than 50 centimeters using symbolic integration utility.

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