Question

program to run on first mission. Usea bine distribution and assign probabies to the posities that Suppose mong of students taking a beginning programming course fail to get the group of such students, al that is c) than on the sumisions (c) Continuing to use this imal model, what is the mean number who will fail? Show My Work

Answer 1

Solution: Let X be the number of students failing to get their first program to run on first submission. This test is done on a group of 6 students. So, 6 trials. Thus, X ~ Bin(6,0.91).

To find the probabilities that

(a) At least 5 fail on their first submission = P(X>=5) = P(X = 5) + P(X = 6) = $\binom{6}{5}(0.91)^5(1-0.91)^1 + \binom{6}{6}(0.91)^6(1-0.91)^0$

= 0.9048466.

(b) Less than 5 fail on their first submission = P(X <5) = P(X<=4) = $\sum^{4} _{x=0}\binom{6}{x}(0.91)^x(1-0.91)^{6-x}$ = 0.09515339

(c) Continuing to use this binomial model, the mean number of students failing = n * p

Here n = no. of students = 66 and p = probability of failure = 0.91

thus, mean = 0.91 * 6 = 5.46

(d) The standard deviation = sqrt(n*p*(1-p)) = sqrt(6*0.91*0.09) = 0.7009993