Question

11. Random samples of size n = 80 were selected from a binomial population with p = 0.2. Use the normal distribution to approximate the following probability. (Round your answer to four decimal places.)

P(p̂ ≤ 0.26)

12. Random samples of size n = 80 were selected from a binomial population with p = 0.8. Use the normal distribution to approximate the following probability. (Round your answer to four decimal places.)

P(p̂ > 0.79)

Answer 1

Please post 1 question per post as per forum rules. Here' the answer to the 1st question, you may use the same logic to arrive at the 2nd

11.

n = 80

p = .20

P(p' <= .26) = ?

We know that when we have to approximate binomial to normal dist we have to use the following formulae to convert the parameters:

Mean = n*p = 80*.20 = 16

Stdev = sqrt(n*p*q) = sqrt(80*.2*.8) = 3.5777

Also, p^ becomes = n*p^ = 80*.26 = 20.8

Now, lets estimate

P(p^<=.26) = P(Z<= (20.8-16)/3.5777)

= P(Z<= .3416) = 0.6337 [Using Z tables to take this out]

Answer is 0.6337