An auditor of Health Maintenance Services reports 40 percent of policyholders 55 years and older submit a claim during the year. Fifteen policyholders are selected at random for company records.

Question

a)how many of the policyholders would you expect to have filed a claim within the last year?
b)what is the probability that 10 of the selected policyholders submitted a claim last year?
c)what is the probability that 10 or more of the selected policyholders filed a claim last year?
d)what is the probability that more than 10 of the selected policyholders filed a claim last year?

Answer 1

Find mean and standard deviation. Use z-scores to find z, then a z-table to find your probability based on the z-score. This is a normal approximation to the binomial distribution.

I'll get you started:

mean or expected value = np = (15)(.40) = ?
standard deviation = √npq = √(15)(.40)(.60) = ?
Note: q = 1 - p

Finish the calculations.
To find z-score:
z = (x - mean)/sd
Note: x = 10

Once you have the z-score, look in a z-table using the score to find your probability. Remember that the question is asking different questions when looking at the table.

Answer 2

Question , what does the letter q represent?