Stat Answer and solving method

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Practice for Test I: Stat 2103 – Feb 2019

Use this information for problems the first four problems. X is a Binomial random variable with eight trials and

a 25% probability of success on each trial. The random variable Y is defined by the following linear function of

X: Y = 10X - 20.

1) What is E(X), the mean of X? a. 1 b. 2 c. 4 d. 8

2) What is E(Y), the mean of Y? a. 0 b. 2.5 c. 10 d. -20

3) What is the standard deviation of X? a. 1.00 b. 1.23 c. 1.50 d. 1.77

4) What is the standard deviation of Y? a. -20 b. -7.75 c. 5.82 d. 12.25

5) Which of the following is not true of a binomial random variable? a. It is based on a fixed number of trials. b. Each trial is independent of all other trials. c. The probability of success changes for each trial. d. The probability distribution may be symmetric.

6) Which of the following is a well-defined random variable?

X P(X) Y P(Y)

-10 0.25 1 0.2

-1 0.5 2 0.4

0 0.25 3 0.2

a. X b. Y c. Both X and Y d. Neither X nor Y

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7) Define the random variable Z as follows. What is E(Z), mean of Z? Z P(Z) 0 0.39

1 0.15

2 0.35

3 0.09

4 0.02

a. 1.0 b. 1.2 c. 1.5 d. 2.5

8) A salesman has a 10% chance of making a sale on each client call. The probability is independent for each call. What is the probability that he makes no sales on a day when he makes five calls?

a. 25% b. 33% c. 59% d. 41%

9) A salesman has a 10% chance of making a sale on each client call. The probability is independent for each call. What is the probability that he makes at least one sale on a day when he makes five calls?

a. 25% b. 33% c. 59% d. 41%

10) Which of the following is a numerical variable? a. The breed of dog owned by pet store customers. b. The state of residence of shoppers at a Manhattan boutique. c. The length of the waiting time for customers at a fast food counter. d. All of the above

For next two problems, use these data values: 8, 9, 8, 9, 6, 7, 1, 3, 9, 10

11) Which of the following statements is true? a. The median is 5.5 b. The median is 6.5 c. The mean is less than the median d. The mean is 8

12) Which of the following statements best describes the shape of this data set? a. Skewed Left b. Skewed Right c. Symmetric d. Bimodal

13) Which of the following data summary measures are not changed by adding a constant to every data value?

a. The mean b. The median c. The standard deviation d. All of the above

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14) The relationship between two numerical variables is graphically displayed by a a. histogram b. bar chart c. pie chart d. scatter plot

Scores Frequency 0-10 1

10-20 1 20-30 1 30-40 2 40-50 5 50-60 5 60-70 19 70-80 22 80-90 56

90-100 48 Total 160

The scores of 160 students on their first statistics exam is displayed above. Use this information to answer the last

four problems.

15) The best guess of the median exam score is a. 93 b. 84 c. 77 d. 68

16) The best guess of the lower quartile of exam scores is a. 93 b. 83 c. 73 d. 63

17) Which of the following statement is true regarding the students’ scores? a. The mean score will be less than the median score b. The mean and median will be equal c. The mean score will be greater than the median score d. The IQR will be greater than 30.

18) Which of the following statements best describes the shape of this data set? a. Skewed Left b. Skewed Right c. Symmetric d. Bimodal

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0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100

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