Statisics 7 questions

1. The following is the time, in minutes, 15 employees of accounting department of East Penn Manufacturing spent commuting to work this morning. [20pts]

28 25 48 37 41 19 32 26 16 23 23 29 36 31 26

1. Organize data into stemplot. [2pts]

1. Find the standard deviation, round it to 2 decimal places. [3pts]

1. Find value of the 85th percentile L85 (or P85) and write its brief interpretation. [3pts]

1. Find Q1, Q3, IQR and test possible outliers. Draw a conclusion clearly. [5pts]

1. Organize data into classes using an interval 15-23 as the first. [2pts]

1. What is a class width w in previous part e? [1pt]

1. Use the frequency table and find the standard deviation. Round the result to two decimal places if necessary. [3pts]

1. Compare results of b) and g). Which one is exact? [1pt]

_________________________________________________________________________________

2. Use the frequency table and find the median. Round only the last result to two decimal places. [4pts]

_________________________________________________________________________________

3. Grace Andrews, a stockbroker, recommends two stocks (Hewlett Packard and Citibank) to her customers. Suppose that the probability that each stock’s price will go up next year is 0.6, and that each stock’s price behavior is independent of the price behavior of the other stock. Take a number of stocks that will go up next year as the random variable X and give a complete probability distribution. [6pts]

4. A survey of executives dealt with their loyalty to the company. One of the questions was, “If you were given an offer by another company equal to or slightly better than your present position, would you remain with the company or take the other position?” The responses of the 200 executives in the survey were cross-classified with their length of service with the company. Give all results rounded to 4 decimal places.[2+3+2+3+1+5=16pts]

a) What is the probability that randomly chosen executive is loyal to the company?

b) What is the probability that randomly chosen executive has more than 10 years of service OR is not loyal to the company?

c) What is the probability that randomly chosen executive has less than one year of service AND is not loyal to the company?

d) Two executives are chosen randomly. What is the probability that both would remain with the company?

e) If an event A means „length of service is more than 10 years“, name its complement A‘.

f) Are events „would remain“ and „1-5 years of service“ independent? Justify your answer numerically and draw a clear conclusion.

5. Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that

Round both final results to four decimal places. State clearly what is a success and what is a failure.

a) of 6 randomly selected patients, exactly 4 will recover? [3pts]

b) of 5  randomly selected patients, at least one will recover? [4pts]

____________________________________________________________________________________

6. A life insurance salesman sells on the average 3 life insurance policies per week. Calculate the probability that: