Q1. A manufacturer knows that 5% of his products are defective if he sells items in

the box of 100 and guarantee that not more than 10 items will be defective. What

is the approximate probability that a box will fail to meet the guaranteed quality?

Ans2. Part-a

Step-1 In the variable view define the variable “X”. In the data view enter the values of

“X” from 0 to 10.

Step-2 To calculate probability distribution under “Transform” menu option choose

“compute variable” option.

Step-3 Under Compute Variable enter Target variable as “P” and for numeric

expression choose the function group “PDF & Noncentral PDF” and under this

group choose “Pdf.Poisson” (under Functions and Special variables) then in

the numeric expression tab enter the values for PDF.POISSON(?,?) as PDF.

POISSON (X,5).

Step-4 In the data view we’ll get the values of P for each value of X.

Step-5 Now, for making the pdf plot: Graphs → Chart Builders → Histogram → Drag X

on

x-axis and P on y-axis → Click on Ok. The histogram will be as follows:-

Ans2. Part-b

Step-1 In the variable view define the variable “X”. In the data view enter the values of

“X” from 0 to 10.

Step-2 To calculate cumulative distribution under “Transform” menu option choose

“compute variable” option.

Step-3 Under Compute Variable enter Target variable as “C” and for numeric

expression choose the function group “CDF & Noncentral CDF” and under this

group choose “Cdf.Poisson” (under Functions and Special variables) then in

the numeric expression tab enter the values for CDF. POISSON (?,?) as CDF.

POISSON (X,5).

Step-4 In the data view we’ll get the values of C for each value of X.

Step-5 Now, for making the cdf plot: Graphs → Chart Builders → Histogram → Drag X

on

x-axis and C on y-axis → Click on Ok. The histogram will be as follows:-

Ans2. Part-c Computing the probability that box will fail to meet the guaranteed quality:-

Step-1 Repeat the steps 1-4 of Part-b of this question.

Step-2 Again go to the Transform menu choose compute variable option.

In the Target Variable write “A” with If condition “X =10”.Write the “1-C” in

numeric expression. Click “Ok”.

The data view will be as follows:-

So, Probability of coming not more than ten items defective from a box of 100 = 0.0137

Q2. Products produced by a machine has 3% defective rate. What is the probability

that the first defect occur in the 5th

item inspected?

Ans3.

Step-1 In the variable view define the variable “X”. In the data view enter the values of

“X” from 0 to 5.

Step-2 To calculate probability distribution under “Transform” menu option choose

“compute variable” option.

Step-3 Under Compute Variable enter Target variable as “P” and for numeric

expression choose the function group “PDF & Noncentral PDF” and under this

group choose “Pdf.Geom” (under Functions and Special variables) then in the

numeric expression tab enter the values for PDF.GEOM(?,?) as PDF.GEOM

(X,0.03).

Step-4 In the data view we’ll get the values of P for each value of X.

Step-5 To calculate the probability that the first defect occur in the 5th

item when

inspected:

Again go to the Transform menu choose compute variable option.

In the Target Variable write “A” with If condition “X =5”.Write the “P” in

numeric expression. Click “Ok”.

The data view will be as follows:

So, the probability that the first defect occur in the 5th

item when inspected =

0.265587843

≈

0.2656