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)
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
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![**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.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8da5c625-81d8-4db3-9f61-2b28dd7af5ea%2F8b24d1b8-eb32-4115-b6be-010632f426e8%2F0egty6_processed.jpeg&w=3840&q=75)
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.*
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