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.
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Checkout Time (minutes)
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Frequency
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Relative Frequency
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Cumulative Relative Frequency
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4.0 - 5.9
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2
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6.0 - 7.9
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0.25
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8.0 - 9.9
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10.0 - 11.9
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1
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12.0 - 13.9
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2
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TOTALS
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12
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1. Complete the frequency table
2. What percent of the checkout times are at least 10 minutes?
3. What percent of the checkout times are between 8 and 10 minutes?
4. What percent of the checkout times are less than 12 minutes?
Problem 2 Using the data from Problem #1 ...
1. Construct a histogram ... you may draw it by hand, if desired.
2. 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 ...
3. Will the mean of the dataset increase, decrease or remain the same and why?
4. Will the median 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 agroup of clients. Answer the following questions.
(a) What is the population?
(b) What is the sample?
(c ) What is the parameter?
(d) What is the statistic ?
(e) What is the variable?
Problem 4 A random sample of starting salaries for an engineer are: $40,000, $40,000, $48,000, $55,000 and $67,000. Find the following and show all work (2 points each). 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 12 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, 12.4, 5.8, 9.7, 8.8, 6.7, 13.2
HINT: DO NOT use EXCEL to calculate quartiles, as the method used by EXCEL is not the same as the standard method we use in our course. It is best to find the quartile values by hand. You should use the approach shown in Example 2.13 (page 87) of the Illowsky text.
(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.
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.
(b) What is the probability of rolling a 2, or 3 or 4 with one die?
(c) You roll both dice, one at a time. What is the probability of rolling a 3with 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?
(e) You roll both dice, one at a time. What is the probability that the second die is greater than 3, given that the first die is an odd number?Think about this one ... it is tricky.
Problem 7 In a box of 100 cookies, 36 contain chocolate and 12 contain nuts. Of those, 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.
(b) What is the probability that a randomly selected cookie contains chocolate?
(c) What is probability that a randomly selected cookie contains chocolate OR nuts? Note, it cannot contain both chocolate and nuts, but must have either chocolate OR nuts.
(d) What is the probability that a randomly selected cookie contains nuts, given that it contains chocolate?
Problem 8 Assume a baseball team has a lineup of 9 batters.
(a) How many different batting orders are possible with these 9 players?
(b) How many different ways can I select the first 3 batters? 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 $40 and another $20. You have to pay $100 if you choose the door with no prize.
(a ) Construct a probability table. See your homework for Illowsky, Chapter 4, #80.
(b) What is your expected winning?
(c) What is the standard deviation of your winning? (HINT: Use the expanded table, similar to your homework, Illowsky, Chapter 4, #80)
Problem 10: Suppose that 85% of graduating students attend their graduation. A group of 22 graduating students is randomlychosen. 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 18 students attend graduation?
(HINT: This is tougher than it looks. You will need use a Binomial Probability Function, so review Illowsky, Chapter 4, #88).