Question

It is known that​ 35% of students change their major in college. In a random sample of

500​ students, what is the probability that less than​ 36% of these students will change their

​major?

A.

0.6808

B.

0.3192

C.

0.0176

D.

0.2000

Answer 1

Solution

Given that,

p = 0.35

1 - p = 1-0.35=0.65

n = 500

= p =0.35

=  [p ( 1 - p ) / n] =   [(0.35*0.65) / 500 ] =

P( <0.36 ) =

= P[( - ) / < (0.36-0.35) / 0.02133]

= P(z <0.47 )

Using z table,   

probability =0.6808