Discuss the following:
Q1: The mean income of a group of sample observations is $500; the standard deviation is $40. According to Chebyshev's theorem, at least what percent of the incomes will lie between $400 and $600?
Q2: The Citizens Banking Company is studying the number of times the ATM located in a Loblaws Supermarket at the foot of Market Street is used per day. Following are the numbers of times the machine was used over each of the last 30 days. Determine the mean number of times the machine was used per day.
83 64 84 76 84 54 75 59 70 61
63 80 84 73 68 52 65 90 52 77
95 36 78 61 59 84 95 47 87 60
Q3: Three defective electric toothbrushes were accidentally shipped to a drugstore by Cleanbrush Products along with 17 nondefective ones. What is the probability the first two electric toothbrushes sold will be returned to the drugstore because they are defective?
Q4: The state of Maryland has license plates with three numbers followed by three letters. How many different license plates are possible?
Q5: The mean starting salary for college graduates in the spring of 2004 was $36,280. Assume that the distribution of starting salaries follows the normal distribution with a standard deviation of $3,300. What percent of the graduates have starting salaries:
a. Between $35,000 and $40,000?
b. More than $45,000?
c. Between $40,000 and $45,000?
Q6: It is estimated that 10 percent of those taking the quantitative methods portion of the CPA examination fail that section. Sixty students are taking the exam this Saturday.
a. How many would you expect to fail? What is the standard deviation?
b. What is the probability that exactly two students will fail?
c. What is the probability at least two students will fail?