Question

Scarlett is practicing math fluency. She has 100 math operation flashcards with 42 addition problem cards, 56 subtraction cards, and 2 multiplication cards. Scarlett will time herself to see how fast she can solve the problems on seven cards. She chooses her seven cards and they are all addition cards. Is choosing all addition cards likely? Explain by running a simulation.

Part A: State the problem or question and assumptions. (2 points)

Part B: Describe the process for one repetition, including possible outcomes, assigned representations, and measured variables. (3 points)

Part C: Use digits from a table of random digits or use your calculator to perform one repetition. Submit the list of random digits and indicate those that represent addition cards. (3 points)

Part D: Suppose there was one repetition when all seven cards were addition cards after 200 repetitions of the simulation. State your conclusions from these results. (2 points)

2.

To increase sales, a cell phone store began giving a free month of service on some cell plan purchases. Customers were unaware whether they would receive the free month until after purchase. The store manager claimed that one in eight customers received the free month. Nine customers each buy a cell phone plan. Let X = the number of customers that receive a free month of cell phone service.

Part A: Is X a binomial random variable? Explain. (3 points)

Part B: What is the mean and standard deviation of X? Provide an interpretation for each value in context. (4 points)

Part C: Three of the nine customers receive a free month of service. Is the store's claim accurate? Compute P(X ≥ 3) and use the result to justify your answer. (3 points)

Answer 1

D.

A.

Yes. Because the experiment satisfies the following conditions.

• A fixed number of trials (9)
• Each trial is independent of the others
• There are only two outcomes ("free month of service" or not)
• The probability of each outcome remains constant from trial to trial. (1/8)

B.

Mean = np

= 9*1/8

= 1.125

It represents the average no. of customers who got the free service month if this experiment is repeated a large no. of times.

Std. deviation =

= 0.9922

It represents the variance among different no. of successes if this experiment is repeated a large no. of times.

C.

P(X = x) = (nCx)*p^x(1-p)^n-x

P(X ≥ 3) = 0.092

Since the probability of atleast 3 customers is 0.092 > 0.05 i.e. it is not unusual and the stores claim is justified.

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