QUESTION 1

The annual rainfall in a certain region is approximately normally distributed with mean 41.7 inches and standard deviation 5.4 inches. Round answers to 4 decimal places. Use Excel to answer these questions. a) What is the probability that a randomly selected year had an annual rainfall of less than 44 inches? C} b) What is the probability that a randomly selected year had an annual rainfall of more than 38 inches? C] c) What is the probability that a randomly selected year had an annual rainfall of between 37 inches and 43 inches? S Suppose approximately 62% of all students study after midnight. For random sample of n = 3 students, let X be the number of students that study after midnight. a. Complete the following table for the binomial distribution of X. Keep at least 4 decimal places. X P(X) 2 3 Determine the mean and standard deviation of X. Keep at least 4 decimal places. b. The expected value of X = C. The standard deviation of X =The followingjoint frequency distribution table shows responses from a sample of 226 unionized employees on how their union president handled a recent labour action. Employees were categorized by age group and by their level of approval. Age Group Approve Disapprcwe Indifferent Total under 25 23 28 2'] 12 25 to 40 3'1 28 3 F! over 40 35 28 24 87 Total 89 84 53 226 Report answers accurate to at least 4 deciml places. 1. What is the probability that a randomly selected employee: a) approved or was indifferent? C] b) was in the 25 1040 age group and approved? d} was in the under 25 age group or was indifferent? C] 2. Given that an employee was in the over 40 age group, what is the probability that the employee approved? C] 3. What is the probability of selecting an employee that was in the under 25 age group given that the employee approved? C]