Question

Consider the probability that fewer than 19 out of 160 students will not graduate on time. Assume the probability that a given student will not graduate on time is 8

1) 0.08
2) 0.92
3) 0.18
4) 0.82

Answer 1

To find the probability that fewer than 19 out of 160 students will not graduate on time, you can use the binomial distribution formula. The answer is 0.82.

Step-by-step explanation:

To find the probability that fewer than 19 out of 160 students will not graduate on time, we can use the binomial distribution formula. Since the probability that a given student will not graduate on time is given as 0.08, the probability of a student graduating on time is 1 - 0.08 = 0.92. Now, we can use the binomial distribution formula:

1. The probability of fewer than 19 students not graduating on time is given by P(X < 19) = P(X = 0) + P(X = 1) + ... + P(X = 18).
   
   Using the binomial distribution formula, where n = 160 (total number of students) and p = 0.92 (probability of graduating on time), we can calculate the probability:
   

P(X < 19) = binompdf(160, 0.92, 18) = approximately 0.9999.

Therefore, the answer is option (4) 0.82.