Hi Belinda,
In part a) you were asked to find the probability that 5 or fewer firms will be found to use LIFO. You found
P(x=5  B(n=15, p=0.2)) = 0.103
which is the probability that exactly 5 firms use LIFO. You need to find
P(x ≤ 5  B(n=15, p=0.2))
= P(x=0  B(n=15, p=0.2)) + P(x=1  B(n=15, p=0.2)) + P(x=2  B(n=15, p=0.2)) +
P(x=3  B(n=15, p=0.2)) + P(x=4  B(n=15, p=0.2)) + P(x=5  B(n=15, p=0.2))
Likewise for the probability that more than 10 firms will be found to use LIFO.
For part b), to plot the probability distribution of x you need to use the table to find
P(x=0) = P(x=0  B(n=15, p=0.2))
P(x=1) = P(x=1  B(n=15, p=0.2))
etc. up to
P(x=15) = P(x=15  B(n=15, p=0.2))
For c), since x is a binomial random variable you can calculate the mean as
mean = n p
and the variance as
variance = n p (1  p).
Penny
