Question

Suppose 52% of the students in a university are baseball players.

If a sample of 411 students is selected, what is the probability that the sample proportion of baseball players will differ from the population proportion by less than 5%? Round your answer to four decimal places.

Answer 1

Solution:

Given that,

n = 411

= 52%=0.52

1 - = 1 - 0.52 = 0.48

=   = 0.52

= ( 1 - ) / n

=   0.52 * 0.48 / 411

= 0.0244

= 0.0244

P(   < 0.05 )

= P ( 0.47< < 0.57 )

=P ( 0.47 - 0.52 / 0.0244 ) < ( -    / ) < ( 0.57 - 0.52 / 0.0244 )

=P ( - 0.05 / 0.0244 < z < 0.05/ 0.0244 )

=P (-2.05 < z < 2.05 )

=P ( z < 2.05) - p ( z < -2.05 )

Using z table

= ( 0.9798 - 0.0202)

= 0.9596

Probability =0.9596