(3) During your summer internship at a candy company, you are responsible for quality control on the foil-wrapping machine used to cover a certain type of chocolate. The ma- chine individually wraps each chocolate in a piece of foil, and seals 25 wrapped chocolates into a box for sale. According to the manufacturer of the machine, the machine should successfully wrap any given chocolate with probability 0.95, independent of past perfor- mance. Your job is to go through five randomly selected boxes of chocolates, and count the number of defective chocolates in each box. (a) If the manufacturer is correct, explain why the number of defective chocolates in each box can be modeled with a Binomial random variable. (b) If the manufacturer is correct, what is the expected number of defective chocolates in any given box. (c) If the manufacturer is correct, what is the probability of finding 3 defective choco- lates or fewer in any given box. (d) If the manufacturer is correct, what is the probability that all five boxes have more than 3 defective chocolates. (e) What does the Central Limit Theorem say about 7, the sampling distribution of number of defective chocolates per box for a sample of five boxes. the average (f) If the manufacturer is correct, use CLT to approximate the probability that z is greater than 3. (g) If all five boxes had more than 3 defective chocolates, would you still believe the manufacturers claim?

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

3) D,E,F,G

(3) During your summer internship at a candy company, you are responsible for quality
control on the foil-wrapping machine used to cover a certain type of chocolate. The ma-
chine individually wraps each chocolate in a piece of foil, and seals 25 wrapped chocolates
into a box for sale. According to the manufacturer of the machine, the machine should
successfully wrap any given chocolate with probability 0.95, independent of past perfor-
mance.
Your job is to go through five randomly selected boxes of chocolates, and count the
number of defective chocolates in each boOx.
(a) If the manufacturer is correct, explain why the number of defective chocolates in
each box can be modeled with a Binomial random variable.
(b) If the manufacturer is correct, what is the expected number of defective chocolates
in any given box.
(c) If the manufacturer is correct, what is the probability of finding 3 defective choco-
lates or fewer in any given box.
(d) If the manufacturer is correct, what is the probability that all five boxes have more
than 3 defective chocolates.
(e) What does the Central Limit Theorem say about 7, the sampling distribution of
the average number of defective chocolates per box for a sample of five boxes.
(f) If the manufacturer is correct, use CLT to approximate the probability that is
greater than 3.
(g) If all five boxes had more than 3 defective chocolates, would you still believe the
manufacturers claim?
Transcribed Image Text:(3) During your summer internship at a candy company, you are responsible for quality control on the foil-wrapping machine used to cover a certain type of chocolate. The ma- chine individually wraps each chocolate in a piece of foil, and seals 25 wrapped chocolates into a box for sale. According to the manufacturer of the machine, the machine should successfully wrap any given chocolate with probability 0.95, independent of past perfor- mance. Your job is to go through five randomly selected boxes of chocolates, and count the number of defective chocolates in each boOx. (a) If the manufacturer is correct, explain why the number of defective chocolates in each box can be modeled with a Binomial random variable. (b) If the manufacturer is correct, what is the expected number of defective chocolates in any given box. (c) If the manufacturer is correct, what is the probability of finding 3 defective choco- lates or fewer in any given box. (d) If the manufacturer is correct, what is the probability that all five boxes have more than 3 defective chocolates. (e) What does the Central Limit Theorem say about 7, the sampling distribution of the average number of defective chocolates per box for a sample of five boxes. (f) If the manufacturer is correct, use CLT to approximate the probability that is greater than 3. (g) If all five boxes had more than 3 defective chocolates, would you still believe the manufacturers claim?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 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