Suppose 91 of all students taking a beginning programming co

Suppose 91% of all students taking a beginning programming course fall to get their first program to run on first submission. Use a binomial distribution and assign probabilities to the possibilities that among a group of 4 such students, (a) at least 3 fail on their first submissions (b) less than 3 fail on their first submissions (c) Continuing to use this binomial model, what is the mean number who will fail? (d) What is the standard deviation?

Solution

(a)

P(X=0) = ⁶C₀ * p^0*(1-p)⁶

= 5.31*10^-7

(b)

P(X>=5) = P(x=5)+P(x=6)

=⁶C₅ * p^5*(1-p)¹+⁶C₆ * p^6*(1-p)⁰

= 0.9048

(c)

P(X<5)=1-0.9048

= 0.09515

(d)

mean = np=6*0.91 = 5.46

variance = np(1-p) = 0.4914

standard eviation = 0.4914 = 0.7009