Homework Problems (Submit to Drop Box for HW 4 by Its Due Day)

Homework problems (submit to Drop box for HW 4 by its due day)

1. Let Y be a binomial random variable with n = 12 and π = 0.3. Find the following values (you may use minitab) : a. P( Y ≤ 4) b. P( Y > 4) you should be able to get this pretty easily, without adding up lots of numbers c. P(Y > 6)

2. The demand of a certain book in a bookstore on any given day is given by the following table (y represents the number of purchases of that book on any given day): y 0 1 2 3 4 5 6 7 P(y) 0.1 0.23 0.31 0.12 0.1 0.05 0.05 0.04

Find: a. The probability that on any given day the demand is more than 4 b. The probability that on any given day the demand is less than or equal to 2 c. On 5 randomly chosen days, what is the probability that 3 of the 5 days have demand more than 4

3. In an inspection of automobiles in a city, 35% of all automobiles had emissions that did not meet EPA regulation. We take a random sample of 10 automobiles. Let X denote the number of automobiles in the sample that fail the inspection. Construct a table that shows the binomial probabilities and cumulative binomial probabilities. It is similar to the last page shown in Viewlet for Lesson 4: “Binomial Probability and Cumulative Probability” in the “Additional Course Resource” folder. [Pay attention to the relation between P(X=x) and P(X <=x).Note that you may use minitab to find the probabilities, etc and then type those in to create the table .] Thus, for this problem, the probability of failing the inspection is 0.35 and there are 10 automobiles. Use the table to answer: a. What is the probability that exactly 2 of the 10 failed the inspection b. What is the probability that 6 or more of the 10 failed the inspection? c. What is the probability that at least 3 of the 10 failed the inspection?

4. Over a long period of time in a large multinational corporation, 20% of all sales trainees are rated as outstanding, 70% are rated as excellent/good, 6% are rated as satisfactory, and 4% are considered unsatisfactory. Compute the probability that 3 out of the 10 trainees are rated as satisfactory or excellent/good.

5. Find a value for z, say z0 , such that P( - z0 < Z < z0) = 0.99.

6. The College Boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean of 500 and a standard deviation of 100. These scores are close to being normally distributed. An exclusive club wishes to invite those scoring in the top 5% on the College Boards to join. a. What score is required to be invited to join the club? b. What score separates the top 70% of the population from the bottom 30%? What do we call this value? [hint: the score that separates the top 20% of the population from the bottom 80% is called the 80th percentile]

7. In a large construction company. 9 workers are randomly selected of which only 3 are female. Is there evidence to doubt that the proportion of female workers is 0.32 or more? (A probability less than a default value of 0.05 is considered doubtful. If the probability is more than 0.05, one fails to doubt.) Note that here it is not appropriate to use the empirical rule approach since the distribution is not close enough to normal distribution. You should use the alternative approach and compute the tail probability as illustrated at the end of Lesson 4.1.