Problem 1 - A random sample of 12 customers was chosen in a supermarket.  The (incomplete) results for their checkout times are shown in the table below.

(a) Complete the frequency table

(b) What percent of the checkout times are 10 minutes or greater?

(c) What percent of the checkout times are between 8 and 9.9 minutes?

(d) What percent of the checkout times are less than 7.9 minutes?

Problem 2 - Using the data from Problem #1 ...

(a) Construct a histogram ... you may draw it by hand, if desired.

(b) In what interval must the median lie?

Assume the largest recorded checkout time was 13.2 minutes. Suppose that data point was incorrect and the actual checkout time was 13.8 minutes. Answer the following ...

(c) Will the median of the dataset increase, decrease or remain the same and why?

(d) Will the mean of the dataset increase, decrease or remain the same and why?

Problem 3 - A fitness center is interested in the mean amount of time a group of clients exercise each week.  A survey will be conducted of a group of clients.  Answer the following questions. There are no numbers for this problem, so you are only explaining your answer in text form.

(a) What is the population of the fitness center?

(b) What is considerd a sample of the fitness center?

(c) What is the parameter that is evaluated for this survey?

(d) What is the test statistic that is evaluated for this survey?

(e) What is the variable for this survey?

Problem 4 - A random sample of starting salaries for an engineer are: $38000, $42000, $44000, $44000, and $52000. Find the following and show all work. Include equations, a table or EXCEL work, to show how you found your solution.

(a) Mean

(b) Median

(c) Mode

(d) Standard Deviation

(e) If a recent graduate is considering a career in engineering, which statistic (mean or median) should they consider when determining the starting salary they are likely to make?  Explain your answer.

Problem 5 - The checkout times (in minutes) for 10 randomly selected customers at a large supermarket during the store's busiest time are as follows:  4.6, 8.5, 6.1, 7.8, 10.7, 9.3, 5.8, 9.7, 8.8, 6.7

(a) What is the mean checkout time?

(b) What is the value for the 25% percentile (first quartile) Q1?

(c) What is the value for the 50% percentile (median)?

(d) What is the value for the 75% percentile (third quartile) Q3?

(e) Construct a boxplot of the dataset. You may draw this by hand, if desired.

Problem 6 - Consider two standard dice where each die has six faces (numbered 1 to 6).

(a) List the number of outcomes in the sample space when you roll both dice. You do not have to show all of the outcomes, but just give the total number.

(b) What is the probability of rolling a 2 or a 4 with one die?

(c) You roll both dice, one at a time. What is the probability of rolling a 1 or 3 with the first die and an EVEN number with the second die?

(d) You roll both dice at the same time. What is the probability the sum of the two dice is less than 5 (total of 4 or less)?

(e) You roll both dice, one at a time. What is the probability that the second die is greater than 4, given that the first die is an even number? Think about this one ... it is tricky.

Problem 7 - You are given a box of 100 cookies. 36 contain chocolate and 12 contain nuts. 8 cookies contain both chocolate and nuts.

(a) Draw a Venn diagram representing the sample space and label all regions. You may draw the diagram by hand, if desired. Be careful with overlapping regions.

(b) What is the probability that a randomly selected cookie contains nuts? 

(c) What is probability that a randomly selected cookie contains chocolate OR nuts?

HINT: This result will be the union of your Venn diagram circles.

(d) What is the probability that a randomly selected cookie contains chocolate, given that it contains nuts? Think about this one ... it is tricky. Use the equation for the Probability of Event B, given Event A.

Problem 8 - Assume a baseball team has a lineup of 9 batters.

(a) How many different batting orders are possible with these 9 players? This is a VERY big number, so think about this one.

(b) How many different ways can I select the first 3 batters out of 9 total players?

HINT: This is a permutation.

(c) Is a "Combination Lock" really a permutation or combination of numbers?  Explain your answer.

Problem 9 - You are playing a game with 3 prizes hidden behind 4 doors. One prize is worth $100, another is worth $20 and another $10. You have to pay $60 if you choose the door with no prize.

(a) Construct a probability table.  See your homework for Illowsky, Chapter 4, #72.

(b) What is your expected winning? This should be the sum of one of your table columns.

(c) What is the standard deviation of your winning? (HINT: Use the expanded table, similar to your homework, Illowsky, Chapter 4, #72)

Problem 10 - Suppose that 90% of graduating students attend their graduation. A group of 30 graduating students is randomly chosen.  Let X be the number of students that attend graduation.  As we know, the distribution of X is a binomial probability distribution. Answer the following:

(a) What are the number of trials (n)?

(b) What is the probability of successes (p)?

(c) What is the probability of failures (q)?

(d) How many students are expected to attend graduation?

(e) What is the probability that exactly 25 students attend graduation?