A waitress believes the distribution of her tips has a model that is slightly skewed to the right, with a mean of $10.40 and a standard deviation of $4.10. She usually waits on about 60 parties over weekend of work. a) Estimate the probability that she will earn at least $700. b) How much does she earn on the best 1% of such weekends? a) P(tips from 60 parties > $700) =O (Round to four decimal places as needed.)
A waitress believes the distribution of her tips has a model that is slightly skewed to the right, with a mean of $10.40 and a standard deviation of $4.10. She usually waits on about 60 parties over weekend of work. a) Estimate the probability that she will earn at least $700. b) How much does she earn on the best 1% of such weekends? a) P(tips from 60 parties > $700) =O (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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![### Problem Statement:
A waitress believes the distribution of her tips has a model that is slightly skewed to the right, with a mean of $10.40 and a standard deviation of $4.10. She usually waits on about 60 parties over a weekend of work.
#### Questions:
a) Estimate the probability that she will earn at least $700.
b) How much does she earn on the best 1% of such weekends?
### Solution Steps:
- For part (a), calculate the probability that the sum of tips from 60 parties exceeds $700. You would typically use a statistical method or a normal approximation to find this probability because the total tip amount is a sum of a large number of independent, identically distributed random variables.
- For part (b), calculate the tip amount corresponding to the top 1% of weekends. This involves determining the 99th percentile of the total distribution of tips over the weekends the waitress waits on 60 parties.
### Answer for part (a):
- Use the placeholder to input the calculated probability, rounded to four decimal places.
\[ \text{a) P(tips from 60 parties > \$700) = } \boxed{\phantom{0}} \]
Please fill in the box with the appropriate probability calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F162b66cd-ff29-4d41-8a2c-9dadd2df5fb7%2Fa5dfe9bd-d145-4006-a278-db518a675e63%2F23bluc_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
A waitress believes the distribution of her tips has a model that is slightly skewed to the right, with a mean of $10.40 and a standard deviation of $4.10. She usually waits on about 60 parties over a weekend of work.
#### Questions:
a) Estimate the probability that she will earn at least $700.
b) How much does she earn on the best 1% of such weekends?
### Solution Steps:
- For part (a), calculate the probability that the sum of tips from 60 parties exceeds $700. You would typically use a statistical method or a normal approximation to find this probability because the total tip amount is a sum of a large number of independent, identically distributed random variables.
- For part (b), calculate the tip amount corresponding to the top 1% of weekends. This involves determining the 99th percentile of the total distribution of tips over the weekends the waitress waits on 60 parties.
### Answer for part (a):
- Use the placeholder to input the calculated probability, rounded to four decimal places.
\[ \text{a) P(tips from 60 parties > \$700) = } \boxed{\phantom{0}} \]
Please fill in the box with the appropriate probability calculation.
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