Question

A survey of U.S. adults found that 8% believe the biggest problem in schools is poor teaching. You randomly select a 1000 sample of U.S. adults. Find the probability that more than 75 U.S. adults believe the biggest problem in school is poor teaching.

Answer 1

Answer :

Given data is :

Sample size n = 1000

P = 8% = 0.08

then q = 1 - p = 1 - 0.08 = 0.92

So,

Mean =

= 1000 * 0.08

= 80

Standard deviation =

=

=

=

therefore,

probability that more than 75 U.S. adults believe the biggest problem in school is poor teaching is : P(X > 75)

i.e P(X > 75) = 1 - P(X < 75) -----------> (1)

Here

Consider,

P(X < 75) = P(Z < (75 - 80) / 8.58)

= P(Z < -5 / 8.58)

= P(Z < - 0.58)

= 0.2810

Substitute in equation 1,we get

P(X > 75) = 1 - P(X < 75)

= 1 - 0.2810

= 0.7190

Hence,the probability that more than 75 U.S. adults believe the biggest problem in school is poor teaching is 0.7190