Question

Consider the probability that no more than 49 out of 140 students will graduate on time. Assume the probability that a given student will graduate on time is 64%.

Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

Answer 1

Solution:

Given that,

P = 0.64

1 - P = 0.36

n = 140

Here, BIN ( n , P ) that is , BIN (140 , 0.64)

then,

n*p = 140*0.64 = 89.6 > 5

n(1- P) = 140*0.36 = 50.4 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 89.6

Standard deviation = =n*p*(1-p) = 140*0.64*0.36 = 32.256

We using countinuity correction factor

P( X a ) = P(X < a + 0.5)

P(x < 49.5) = P((x - ) / < (49.5 - 89.6) /32.256 )

= P(z < -7.06)

= 0.0000

Probability = 0

The probability that no more than 49 out of 140 students will graduate on time is 0.0000