Question

Suppose that Dr. Goodgrader fails p = 35% of his students. She now has a class of 200 students. Use the normal approximation to the binomial distribution to estimate the probability that she fails 66 or fewer students.

Answer: 0.3015 - Need work

Answer 1

Solution

Given that,

p = 0.35

1 - p = 1 - 0.35 = 0.65

n = 200

= p = 0.35

=  [p ( 1 - p ) / n] =   [(0.35 * 0.65) / 200 ] = 0.04

x = 66

= x / n = 66 / 200 = 0.33

P( < 0.33)

= P[( - ) / < (0.33 - 0.35) / 0.04 ]

= P(z < -0.50)

Using z table,

= 0.3085