Q1. Ten coins are thrown simultaneously. Consider the following questions:

a. Find the probability distribution of number of heads obtained and draw a

histogram.

b. Find cdf and make cdf plot.

c. Find the probability of getting atleast 7 heads.

Ans1. Part-a

Step-1 In the variable view define the variable “X” for number of heads when ten coins

are thrown simultaneously. 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.Binom” (under Functions and Special variables) then in the

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

PDF.BINOM(X,10,0.5).

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:-

Ans1. Part-b

Step-1 In the variable view define the variable “X” for number of heads when ten coins

are thrown simultaneously. 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.Binom” (under Functions and Special variables) then in

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

CDF.BINOM(X,10,0.5).

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:-

Ans1. Part-c

Step-1 Repeat the steps 1 to 4 of part-a.

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

In the Target Variable write “A” (which stands for proababilty (X≥7)), in the

numeric expression write “P” along with If condition “X ≥ 7”.

The data view will be as follows:

Step-3 To find P(X ≥ 7) follow as:

Analyze menu → Descriptive Analysis → Frequencies → Move variable A

from left side to right side → choose Statistics → under central tendencies

mark sum →click continue → click ok.

The result will be as follows:

So, the probability of getting atleast 7 heads = 0.1719