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? b) At least 2 cancellations/reschedules? c) Find the mean (round to 1 decimal place) d) Find the standard deviation (round to 1 decimal place) [2 marks] [4 marks] [1 mark] [1 mark] 2. (x) (y) 4 6 3372222 10 12 20 15 20 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: a) P (0 z < 1.33) b) P (z > 0.21) c) P (-1.07 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]