×
Log in to StudySoup
Get Full Access to Elementary Statistics: Picturing The World - 6 Edition - Chapter 4.3 - Problem 16e
Join StudySoup for FREE
Get Full Access to Elementary Statistics: Picturing The World - 6 Edition - Chapter 4.3 - Problem 16e

Already have an account? Login here
×
Reset your password

Solution: Using a Distribution to Find Probabilities In

Elementary Statistics: Picturing the World | 6th Edition | ISBN: 9780321911216 | Authors: Ron Larson; Betsy Farber ISBN: 9780321911216 66

Solution for problem 16E Chapter 4.3

Elementary Statistics: Picturing the World | 6th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Elementary Statistics: Picturing the World | 6th Edition | ISBN: 9780321911216 | Authors: Ron Larson; Betsy Farber

Elementary Statistics: Picturing the World | 6th Edition

4 5 1 338 Reviews
15
4
Problem 16E

Problem 16E

Using a Distribution to Find Probabilities In Exercise, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Precipitation In Savannah, Georgia, the mean number of days in July with 0.01 inch or more of precipitation is 13. Find the probability that, next July, the number of days with 0.01 inch or more of precipitation in Savannah is (a) exactly 16 days, (b) at most 16 days, and (c) more than 16 days.

Step-by-Step Solution:
Step 1 of 3

Solution 16E

Step1 of 4:

From the given problem we have an experiment, In that the mean number of days in July with 0.01 inch or more of precipitation is 13.

Here our goal is:

a). We need to find the probability that the number of days with 0.01 inch or more of precipitation in Savannah is exactly 16 days.

b). We need to find the probability that the number of days with 0.01 inch or more of precipitation in Savannah is at most 16 days. 

c). We need to find the probability that the number of days with 0.01 inch or more of precipitation in Savannah is more than 16 days.


Step2 of 4:

a).

Let,

Let us consider a random variable ‘x’ it presents the number of days in July with 0.01 inch or more of precipitation. And here ‘x’ follows the Poisson distribution with parameters ’. The probability mass function of the Poisson distribution is:

The probability that the number of days with 0.01 inch or more of precipitation in Savannah is exactly 16 days is:

 

                               

             

Therefore, P(X = 16) = 0.072.


Step3 of 4:

b).

The probability that the probability that the number of days with 0.01 inch or more of precipitation in Savannah is at most 16 days is:

Where,

is obtained from excel by using the function:

“=Poisson(x,  false)”.

X

0

2.26033E-06

1

2.93843E-05

2

0.000190998

3

0.000827657

4

0.002689886

5

0.006993704

6

0.015153025

7

0.028141333

8

0.045729666

9

0.066053962

10

0.085870151

11

0.101482905

12

0.109939814

13

0.109939814

14

0.10208697

15

0.088475374

16

0.071886242

Total

0.835493148

Now,

     

Therefore,


Step4 of 4:

c).

The probability that the probability that the number of days with 0.01 inch or more of precipitation in Savannah is more than 16 days is:

From part (b), we have

 

               

               

Therefore,


Step 2 of 3

Chapter 4.3, Problem 16E is Solved
Step 3 of 3

Textbook: Elementary Statistics: Picturing the World
Edition: 6
Author: Ron Larson; Betsy Farber
ISBN: 9780321911216

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Solution: Using a Distribution to Find Probabilities In