The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $16. Find the probability that a randomly selected utility bill is (a) less than $67, (b) between $87 and $120, and (c) more than $130. (a) The probability that a randomly selected utility bill is less than $67 is (Round to four decimal places as needed.) (b) The probability that a randomly selected utility bill is between $87 and $120 is (Round to four decimal places as needed.) (c) The probability that a randomly selected utility bill is more than $130 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 $16. Find the probability that a randomly selected utility bill is (a) less than $67, (b) between $87 and $120, and (c) more than $130. (a) The probability that a randomly selected utility bill is less than $67 is (Round to four decimal places as needed.) (b) The probability that a randomly selected utility bill is between $87 and $120 is (Round to four decimal places as needed.) (c) The probability that a randomly selected utility bill is more than $130 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 in Utility Bills
The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $16. We need to find the probability that a randomly selected utility bill falls into specific ranges.
**Problem Breakdown:**
1. **Find the probability that a randomly selected utility bill is less than $67.**
\[ (a) \text{The probability that a randomly selected utility bill is less than } \$67 \text{ is } \boxed{\hspace{2cm}}. \]
- (Round to four decimal places as needed.)
2. **Find the probability that a randomly selected utility bill is between $87 and $120.**
\[ (b) \text{The probability that a randomly selected utility bill is between } \$87 \text{ and } \$120 \text{ is } \boxed{\hspace{2cm}}. \]
- (Round to four decimal places as needed.)
3. **Find the probability that a randomly selected utility bill is more than $130.**
\[ (c) \text{The probability that a randomly selected utility bill is more than } \$130 \text{ is } \boxed{\hspace{2cm}}. \]
- (Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febc6c9e4-20c2-4aa0-9f79-b773de998cf1%2F11c94d5a-f061-49e2-a685-252806df9810%2Flime2a8_processed.png&w=3840&q=75)
Transcribed Image Text:#### Understanding Normal Distribution in Utility Bills
The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $16. We need to find the probability that a randomly selected utility bill falls into specific ranges.
**Problem Breakdown:**
1. **Find the probability that a randomly selected utility bill is less than $67.**
\[ (a) \text{The probability that a randomly selected utility bill is less than } \$67 \text{ is } \boxed{\hspace{2cm}}. \]
- (Round to four decimal places as needed.)
2. **Find the probability that a randomly selected utility bill is between $87 and $120.**
\[ (b) \text{The probability that a randomly selected utility bill is between } \$87 \text{ and } \$120 \text{ is } \boxed{\hspace{2cm}}. \]
- (Round to four decimal places as needed.)
3. **Find the probability that a randomly selected utility bill is more than $130.**
\[ (c) \text{The probability that a randomly selected utility bill is more than } \$130 \text{ is } \boxed{\hspace{2cm}}. \]
- (Round to four decimal places as needed.)
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