Suppose a widget machine has a 3% defective rate. This means that 3% of the widgets produced by the machine are defective on average. Suppose we randomly select widgets produced by this machine one by one. Let X equal the number widgets we select until we get our 1st defective widget. Let Y equal the number of widgets we select until we get our 2nd defective widget. a. What is the probability that the 1st defective widget occurs on the 1st trial? b. What is the variance of X? c. What is the probability that X > 13? d. What is the probability that X s 13? e. What is the probability that Y = 8? f. What is the probability that Y = 20? g. What is the smallest value k, such that the probability of finding a defective widget by trial k is at least .69? Add any comments below.

Suppose a widget machine has a 3% defective rate. This means that 3% of the widgets produced by the machine are defective on average. Suppose we randomly select widgets produced by this machine one by one. Let X equal the number widgets we select until we get our 1st defective widget. Let Y equal the number of widgets we select until we get our 2nd defective widget. a. What is the probability that the 1st defective widget occurs on the 1st trial? b. What is the variance of X? c. What is the probability that X > 13? d. What is the probability that X s 13? e. What is the probability that Y = 8? f. What is the probability that Y = 20? g. What is the smallest value k, such that the probability of finding a defective widget by trial k is at least .69? Add any comments below.

Name: **Widget Defect Probability and Statistics***Overview:*Suppose a widg
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Description: **Widget Defect Probability and Statistics***Overview:*Suppose a widget machine has a 3% defective rate. This means that 3% of the widgets produced by the machine are defective on average. Suppose we randomly select widgets produced by this machine

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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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

**Widget Defect Probability and Statistics**

*Overview:*

Suppose a widget machine has a 3% defective rate. This means that 3% of the widgets produced by the machine are defective on average. Suppose we randomly select widgets produced by this machine one by one.

- Let $ X $ equal the number of widgets we select until we get our 1st defective widget.
- Let $ Y $ equal the number of widgets we select until we get our 2nd defective widget.

*Questions:*

a. What is the probability that the 1st defective widget occurs on the 1st trial?
b. What is the variance of $ X $?
c. What is the probability that $ X > 13 $?
d. What is the probability that $ X \leq 13 $?
e. What is the probability that $ Y = 8 $?
f. What is the probability that $ Y = 20 $?
g. What is the smallest value $ k $, such that the probability of finding a defective widget by trial $ k $ is at least 0.69?

*Note:*

Add any comments below this section.

*Data and Work Area:*

Use the space provided for calculations and notes.

*Tools:*

Students may use statistical calculators or programs to find probabilities and variances.

Remember to apply relevant formulas for geometric and negative binomial distributions.

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Please help me fix problem D,E,F, Thank you!