Question

A research institute reports that 73% of workers reported that they​ and/or their spouse had saved some money for retirement. Complete parts a and b below.

a.) If a random sample of 30 workers is​ taken, what is the probability that fewer than 16 workers​ and/or their spouses have saved some money for​ retirement?

b.) If a random sample of 60 workers is​ taken, what is the probability that more than 48 workers​ and/or their spouses have saved money for​ retirement?

THANKS!

Answer 1

The proportion of workers who reported that they and/or their spouse had saved some money for retirement is given here as 0.73.

a) The number of workers out of 30 who have saved some money for retirement is modelled here as:

Therefore the probability required here is:
P(X < 16)

This can be computed in EXCEL here as:
P(X <= 15)

This is computed in EXCEL here as:
=binom.dist(15,30,0.73,TRUE)

The output here is

0.00607844

Therefore 0.006078 is the required probability here.

b) Now for a sample size of 60 workers, the probability that more than 48 workers​ and/or their spouses have saved money for​ retirement is computed here as:

P(X > 48) = 1 - P(X <= 48)

=1-BINOM.DIST(48,60,0.73,TRUE)

The output here is given as:

0.082146

Therefore 0.082146 is the required probability here.