Question

8. Seventy-five percent of the students graduating from high school in a small town in Oklahoma attend college. For a random sample of 50 students from the town, what is the probability that

a. at least 80% of the surveyed students will attend college?

b. between 80% and 85% (inclusive) of the surveyed students will attend college?

please explain thought process and step by step

Answer 1

Solution

Given that,

p = 0.75

1 - p = 1 - 0.75=0.25

n = 50

= p =0.75

=  [p( 1 - p ) / n] = [(0.75*0.25) /50 ] = 0.0612

P( > 0.80) = 1 - P( <0.80 )

= 1 - P(( - ) / < (0.80 - 0.75) / 0.0612)

= 1 - P(z <0.82 )

Using z table

= 1 -0.7939

=0.2061

(B)

P(0.80< < 0.85)= P[(0.80 - 0.75) /0.0612 < ( - ) / < (0.85 - 0.75) /0.0612 ]

= P( 0.82< z <1.63 )

= P(z <1.63 ) - P(z < 0.82)

Using z table,   

= 0.9484 -0.7939

=0.1545