2.A city department has introduced a quality improvement program and has allowed employees to get credit for overtime hours when attending the meetings of their quality groups. The total number of overtime meeting hours, for each of the 26 pay periods in one year by now, were: 30, 100, 100, 96, 194, 163, 65, 41, 100, 43, 96, 100, 80, 42, 100, 75, 95, 65, 43, 163, 41, 41, 80, 114, 30, 114

(a) Find the mean of the overtime hours.

(b) Complete the table and find the variance and standard deviation.

3. The number of days the first 22 heart transplant patients at Stanford survived after their operation were: 3, 15, 20, 23, 26, 32, 32, 32, 46, 48, 48, 56, 64, 68, 69, 69, 70, 71, 71, 80, 85, 125

(a) Find the median.

(b) Find the 90𝑡ℎ90th percentile.

(c) Find the first and the third quartile.

(d) Is there any outlier in this data set?

(e) Construct a box plot.

4.The medical records of the 445 male diabetics patients reporting to a clinic during one year provide the following results:

Find the probability that:

(a) The age of the patients is above 40 and their parents are not diabetics.

(b) The age of the patients is above 40 or their parents are not diabetics.

(c) The age of the patients is above 40 given that their parents are not diabetics.

(d) The age of the patients is between 20 and 40 or their parents are diabetics.

If 𝐴=A=”The age of the patient is below 20” and 𝐵=B=”Patient’s parents are diabetics”.

(e) Are events A and B independent? Justify tour answer.

(f) Are events A and B mutually exclusive? Justify tour answer.

5. According to the Mendelian theory of inherited characteristics, a cross fertilization of related species of red- and white- flowered plants produces a generation whose offspring contain 25% red-flowered plants. Suppose that a horticulturist wishes to cross 7 pairs of the cross-fertilized species. Of the resulting 5 offspring, what is the probability that:

(a) Let 𝑋=X= the number of red-flowered plants. What is the probability distribution of 𝑋X?

(b) There will be no red-flowered plant.

(c) There will be 4 or more red-flowered plants.

(d) Find the expected value, variance and the standard deviation of 𝑋X.

6. The Colorall Paint factory uses “agent A” in the paint manufacturing process. There is an average of 3.45 particles of agent A in a cubic metre of the air emitted during the production process.

(a) Let 𝑋=X= the number of particles of agent A in a cubic metre of the air emitted. What is the probability distribution of 𝑋X?

(b) What is the probability that there will be five particles of agent A in a cubic metre of air emitted from the factory?

(c) What is the probability that there will be at least four particles of agent A in a cubic metre of air emitted from the factory?

(d) Find the expected value, variance and the standard deviation of 𝑋X.