The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $15. Find the probability that a randomly selected utility bill is (a) less than $68, (b) between $85 and $120, and (c) more than $150 (a) The probability that a randomly selected utility bill is less than $68 is (Round to four decimal places as needed) (b) The probability that a randomly selected utility bill is between $85 and $120 is (Round to four decimal places as needed.) (c) The probability that a randomly selected utility bill is more than $150 is (Round to four decimal places as needed)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Question

Answer all three

**Understanding Normal Distribution - Utility Bills Example**

The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $15. We need to find the probability that a randomly selected utility bill is:
  
- **(a)** less than $68.
- **(b)** between $85 and $120.
- **(c)** more than $150.

**Solution Approach:**

To solve these problems, we will use the properties of the normal distribution. The Z-score formula will be used to find probabilities:

\[ Z = \frac{X - \mu}{\sigma} \]

where \( X \) is the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.

**Questions:**

**(a)** The probability that a randomly selected utility bill is less than $68 is [ ]  
*Round to four decimal places as needed.*

**(b)** The probability that a randomly selected utility bill is between $85 and $120 is [ ]  
*Round to four decimal places as needed.*

**(c)** The probability that a randomly selected utility bill is more than $150 is [ ]  
*Round to four decimal places as needed.*
Transcribed Image Text:**Understanding Normal Distribution - Utility Bills Example** The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $15. We need to find the probability that a randomly selected utility bill is: - **(a)** less than $68. - **(b)** between $85 and $120. - **(c)** more than $150. **Solution Approach:** To solve these problems, we will use the properties of the normal distribution. The Z-score formula will be used to find probabilities: \[ Z = \frac{X - \mu}{\sigma} \] where \( X \) is the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. **Questions:** **(a)** The probability that a randomly selected utility bill is less than $68 is [ ] *Round to four decimal places as needed.* **(b)** The probability that a randomly selected utility bill is between $85 and $120 is [ ] *Round to four decimal places as needed.* **(c)** The probability that a randomly selected utility bill is more than $150 is [ ] *Round to four decimal places as needed.*
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman