Question

Consider the probability that at most 93 out of 127 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 53%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

the answer will be in yes or no format

Answer 1

Solution :

Given that,

p = 0.53

q = 1 - p = 0.47

n = 127

Using binomial distribution,

= n * p = 127 * 0.53 = 67.31

= n * p * q = 127 * 0.53 * 0.47 = 4.6246

Using continuity correction ,

= P((x - ) / < (93.5 - 67.31) / 4.6246)

= P(z < 5.66)

= 1

Probability = 1