Thanks and Best Regards

Belinda

In a survey of 15 manufacturing firms, the number of firms that use LIFO (a last-in first-out accounting procedure for inventory) is a binomial random variable x with n=15 and p=0.2.

a) What is the probability that five or fewer firms will be found to use LIFO? Is it unlikely that more than 10 firms will be found to use LIFO? Comment.

The probability that five or less firms use LIFO:

P(x=5 | B(n=15, p=0.2)) = 0.103

The probability that 10 firms use LIFO:

P(x=10 | B(n=15, p=0.2)) = 0+

b) Plot the probability distribution of x. Is the distribution highly skewed?

c) What are the mean and the standard deviation of x. What is the coefficient of variation of x?
What would be the value of this coefficient if 150 firms were surveyed rather than 15 (continue to assume that p=0.2)? Describe the effect of the larger survey on the relative variability of x.

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