Question

A university administrator expects that 30% of students in a core course will receive an A. He looks at the grades assigned to 100 students. The probability that the proportion of students that receive an A is 0.25 or less is ________.

Answer 1

Solution

Given that,

p = 0.30

1 - p = 1 -0.30 =0.70

n = 100

= p = 0.30

=  [p ( 1 - p ) / n] =   [0.30*(0.70) / 100 ] = 0.0458

P( ≤ 0.25 )

= P[( - ) /    ≤ (0.25 -0.30 / 0.0458]

= P(z   ≤ -1.09 )

= 0.1379

probability = 0.1379