Q1. A national newspaper reported that employees of most companies have an average balance of $38,000 in their 401K accounts. Joe Schmoe, the CEO of Widget Company of America, feels that his employees have a higher balance than the average reported by the newspaper. He samples 10 of his employees and finds the following amounts:
$8,600 $36,700 $82,100 $24,500 $44,200 $61, 400 $14,300 $11,000 $9,200 $84,800
a. What is the mean of the data?
b. What is the median of the data?
c. What is the sample standard deviation of the data?
Q2. A local church is studying the amount of offerings in an envelope from their early Sunday morning's services. The church studied 500 envelopes and found the following:
Less than $5 200
$5 to $9.99 100
$10 to $19.99 75
$20 to $49.99 75
$50 or more 50
a. What is the probability of opening one envelop and finding $20 or more in it?
b. What is the probability of opening one envelop and finding less than $10 in it?
c. What is the probability of opening two envelopes and finding less than $5 in each one of them?
Q3. A class of 13 students is trying to decide how they should form themselves into groups of 4 for an upcoming classroom activity. One of the students first proposes they calculate how many combinations of 4 students can be made from 13 people. After doing the calculations, how many groups of 4 people can be made from a student population of 13 people?
Q4. The top salesperson of Floor coverings of Tampa insists she has a 65 percent chance of selling a floor covering to any customer she talks to during a normal workday. If She talks to 15 customers today
a. What is the probability she will sell exactly 7 floors?
b. What is the probability she will sell more than 10 floors?
c. What is the probability she will sell less than 9 floors?
Q5. A local tire retailer has determined that his XL100 tire has a mean lifetime of 70,000 miles. Over the years, he has found that the lifetime of the tire actually follows a normal distribution with a standard deviation of 12,000 miles. Based upon his analysis
a. What percent of the tires will last less than 50,000 miles?
b. What percent of tires will last more than 80,000 miles?
c. What percent of tires will last between 62,000 miles and 82,000 miles?
d. Ten percent of the tires will last more than what number of miles?
Q6. Frank Schmuck works for a beverage distribution company. From experience, he understands there is a 15 percent chance he will receive a slight shock whenever he does maintenance on a beverage dispensing machine. Frank is scheduled to work on 8 machines today.
a. What is the probability he will receive a shock on just the first and last machines he works on?
b. What is the probability he will not receive a shock from any of the machines?
c. Frank just finished working on the 7th machine and he has not yet received a shock. What is the probability he will be shocked on the 8th machine?