Question

A government study concluded that 45% of people receiving Social Security payments also receive retirement income from a private IRA. We decided to take a sample of 200 people receiving Social Security payments and asked them if they also receive retirement income from a private IRA. Define the random variable x to be the number of people who also receive retirement income from a private IRA.

Showing your work in Excel as demonstrated in class, what is the probability that x is:

Exactly 100?

Exactly 85?

Greater than or equal to 80?

Greater than 80?

Between 78 and 83, inclusive?

Between 100 and 200, inclusive?

Answer 1

Solution:

We are given,

p = probability of success = 0.45

n = Sample size = 200

a) P( x = 100 ) = .............?

Excel formula: =BINOMDIST(100,200,0.45,FALSE)

P( x = 100 ) = 0.0206

b) P( x = 85 ) = .............?

Excel formula: =BINOMDIST(85,200,0.45,FALSE)

P( x = 85 ) = 0.0442

c) P( x 80 ) =........?

P( x 80 ) = 1 - P( x 79 ) =

Excel formula: =1-BINOMDIST(79,200,0.45,TRUE)

P( x 80 ) = 0.9327

d) P( x > 80 ) =........?

P( x > 80 ) = 1 - P( x 80 ) =

Excel formula: =1-BINOMDIST(80,200,0.45,TRUE)

P( x 80 ) = 0.9119

e) P( 78 x 83 ) =..........?

P( 78 x 83 ) = P( x 83 ) - P( x < 78 )

P( 78 x 83 ) = P( x 83 ) - P( x 77 )

Excel formula: =BINOMDIST(83,200,0.45,TRUE) - =BINOMDIST(77,200,0.45,TRUE)

P( 78 x 83 ) = 0.1406

f)

P( 100 x 200 ) =..........?

P( 100 x 200 ) = P( x 200 ) - P( x < 100 )

P( 100 x 200 ) = P( x 200 ) - P( x 99 )

Excel formula: =BINOMDIST(200,200,0.45,TRUE) - =BINOMDIST(99,200,0.45,TRUE)

P( 100 x 200 ) = 0.0887

Done