In Stat 151 course at MacEwan University, we consider a sample with the following data values: 1, 2, 2, 3, 3, 3, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 13, 15, 15, 23, 65 (If needed: P xi = 228, P x 2 i = 6155) (a) Find Q1, Q2, Q3, lower limit and upper limit. [4 marks] (b) Construct a boxplot for this data. Identify any outlier(s). [4 marks] (c) Find the mean and standard deviation of this data. [4 marks] (d) Which measurement is proper for the centre of this data set? [2 marks] 2. (3 marks) In Stat 151 course at MacEwan University, the professor gives students data set A as follows. Set A: 7, 9, 10, 11, 13. Another three sets of data, set X, Y and Z are shown below: Set X : -7,-9,-10,-11,-13 Set Y : 14, 18, 20, 22, 26 Set Z : 9, 11, 12, 13, 15. Without calculating the standard deviation for any of the above sets, explain clearly which of the sets X, Y or Z has the same standard deviation as that of Set A. 2 3. (12 marks). A student from Stat 151 AS 03 at MacEwan University conducted a survey on a selected sample of male and female grade 12 students. Students were asked if they like mathematics. The following table shows the responses of these students: Yes No Total Male 30 90 120 Female 40 80 120 Total 70 170 240 (i) If one person is selected at random what is the probability: (a) The person answers yes and is a male. [2 marks] (b) The person answers yes or is a male. [2 marks] (c) The person is a female given she says yes. [2 marks] (ii) Are the events female and yes independent? [4 marks] (ii) Are the events male and no mutually exclusive? [2 marks] 4. (8 marks) After graduated from MacEwan University, Bob applied for company A and company B. The following two tables provide the actual wages paid to 100 employees in each company. Weekly Wage ($) Company A 200 250 400 1400 Number of employees earning this wage 40 32 24 4 Weekly Wage ($) Company B 200 250 300 600 Number of employees earning this wage 10 40 45 5 (a) Find the average wage for each company. [4 marks] (b) What weekly wage do most of the employees earn in each company? [2 marks] (c) Which company should Bob choose? [2 marks] 3 5. (4 marks). The probability to win a game is 0.03. If Bob played the game 10 times, find the probability that Bob will win at least twice. 6. (8 marks). Suppose that the midterm grade of students in a math course is normally distributed with mean 80 and standard deviation 8. (a) Find the minimum grade that a student needs to be the top 5% of all students. [2 marks] (b) Find the probability that a randomly selected students grade is between 72 and 85. [2 marks] (c) What is he probability that the sampling error made in estimating the population mean grade of all students by the mean grade of a sample of 16 students will be at most 3? [4 marks] 7. (5 marks) The probability of a student eating cereal as breakfast is 2/3. Consider only 2 independent students and let X be the number of students eating cereal as breakfast. What is the probability distribution of X? 8. (6 marks) Sarah has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will raise in price, and a 60% chance that fund B will raise in price, given that fund A raises in price. There is also a 30% chance that fund B will raise in price. What is the probability that NONE of the funds will raise in price? 4