The Binomial Distribution Worksheet (Page 6 of 6) in pdf

The Binomial Distribution Worksheet Page 6

Exercise 2. A multiple choice test has 25 questions each of which has 5 possible answers, only one of

which is correct. If Judy guesses on all questions, what is the probability that she will answer more than

15 questions correctly (i.e. she will pass the test)

Exercise 3. According to a published study, 1 in every 7 men has been involved in a minor traffic

accident. Suppose we have randomly and independently sampled twenty-five men and asked each

whether he has been involved in a minor traffic accident. How many of the 25 men do we expect to

have never been involved in a minor traffic accident?

Exercise 4 (4.51, p. 210). According to the Canadian Journal of Information and Library Science (Vol.

33, 2009), nearly 90% of workers in law libraries are satisfied with their job. Assume the true

proportion of law librarians in Canada who are satisfied with their job is .9. In a random

sample of 20 law librarians in Canada, what is the probability that at most 2 are unsatisfied with their

job?

Exercise 5 (4.55, p. 211). According to the National Bridge Inspection Standard (NBIS), public bridges

over 20 feet in length must be inspected and rated every 2 years. The NBIS rating scale ranges from 0

(poorest rating) to 9 (highest rating). University of Colorado engineers used a probabilistic model to

forecast the inspection ratings of all a major bridges in Denver (Journal of Performance of Constructed

Facilities, Feb. 2005). For the year 2020, the engineers forecast that 9% of all a major Denver bridges

will have ratings of 4 or below.

a. Use the forecast to find the probability that in a random sample of 10 major Denver bridges, at least

3 will have an inspection rating of 4 or below in 2020.

b. Suppose that you actually observe 3 or more of the sample of 10 bridges with inspection ratings of

4 or below in 2020. What inference can you make? Why?

The Binomial Distribution Worksheet Page 6