1.A hospital administrator found that 28% of surgeries from last year were cancelled or rescheduled. What is the probability that for a group of 12 surgeries, that were will be: (Express your answers correct to 4 decimal places):

a) Exactly 4 cancellations/reschedules? [2 marks]

b) At least 2 cancellations/reschedules? [4 marks]

c) Find the mean (round to 1 decimal place) [1 mark]

d) Find the standard deviation (round to 1 decimal place) [1 mark]

2.

(x)	(y)
4	35
6	31
10	22
12	20
15	15
20	12

a) Plot the data on a scatter plot. Use software for this part. [2 marks]

b) Find the equation of the line of best fit.Round off the coefficients to 2 decimal places. [5 marks]

c) Calculate the linear correlation coefficient to 3 decimal places. [2 marks]

3. Find the following probabilities: [6 marks]

a) P (0 < z < 1.33)

b) P (z > 0.21)

c) P ( -1.07 < z < 1.53)

4.A national survey found that college students work an average of 28 hours per week. Assuming that the number of hours worked is approximately normally distributed with a standard deviation of 3.5 hours,

a) what proportion of college students work more than 22 hours? [3 marks]

b) how many hours do students, in the middle 50% of the population, work? Round the answers to one decimal place. [6 marks]

5. According to a recent report, the national average salary for a software engineer was $90,889. Assume the standard deviation is $8100. Find the probability that for the mean of a random sample of 32 software engineers will have a mean greater than $88000. [3 marks]