# Middlesex County College Business Analytics Worksheet

Population and samples and variables

Probability and percentage

Discrete distribution

Binomial distribution

Contingency tables

Mean median mode range standard deviations coefficient variations and Z score

independent/dependent covariance and correlation between x and y

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22 points

1.[22 pt.] Compute the following probabilities.

1.1) [7 pt.] 6 cards are drawn from the deck successively at random and without replacement. Let A be the event of two spades appears in the first five draws. Let B be the event

of a spade on the sixth draw. The probabilities of the two events are known as P{A} = 0.274280 and P[B]A} = 0.234043. What is the probability of the third spade appears on the

sixth draw?

1.2) [7 pt.] A roulette wheel has numbers from 1 to 20, as well as 0 and 00. When an odd number comes up, you win $2; otherwise, you lose $2. What is the expected gain (or loss)

from a single trial? What is the variance of the gain (or loss)?

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1.3) (8 pt.] A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the

questions. She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randovaly selects one ball for each question and replaces the ball

in the box. The marking on the ball will determine her answer to the question. There are five multiple-choice questions on the exam. What is the probability that she will get less

than four correct answers?

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39 points

2. [39 pt.] Energy drink consumption has continued to gain in popularity since the 1997 debut of Red Bull, the current leader in the energy drink market. Given below are the

exam scores in Statistics and Marketing courses and the number of 12-oz. energy drinks consumed within a week prior to the exams of 5 college students (assume that the two

exams were on the same date).

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39 points

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2. [39 pt.] Energy drink consumption has continued to gain in popularity since the 1997 debut of Red Bull, the current leader in the energy drink market. Given below are the

exam scores in Statistics and Marketing courses and the number of 12-oz. energy drinks consumed within a week prior to the exams of 5 college students (assume that the two

exams were on the same date).

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Marketing exam

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2.1) [6 pt.] Compute the sample means of the exam scores in each course.

2.2) [6 pt.] Compute the sample variance of the exam scores in each course.

2.3) [7 pt.] Compute the Z score of a new observation, Marketing exam score[58. Is the new observation an outlier?

2.4) [7 pt.] Given the sample dataset, what is the sample covariance between the exam scores of Statistics course and the number of drinks consumed?

2.5) [7 pt.] Given the sample dataset, what is the sample correlation coefficient between the exam scores of Marketing course and the number of drinks consumed?

2.6) [6 pt.] In which course would such energy drinks be more effective in preparing the exam? Also, provide the reason to support your answer.

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19 points

3. (19 pt. ] Suppose that we have the following dataset: (2.5, 1.8, 8.5, 3.5, 2.4, 1.6, 3.0, 4.2, 6.0).

3.1) (7 pt.] Find five number summaries (X, 1st quartile, 2nd quartile, 3rd quartile)

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3.2) [6 pt.] Find the range and inter-quartile range (IQR).

3.3) [6 pt.] Is distribution of this dataset (i) symmetric, (ii) left-skewed or (iii) right-skewed? Also, provide the reason to support your answer.

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2 points

4.1) (2 pt.] If a simple random sample is chosen with replacement, everyone has the same chance of selection on every selection.

O True

O False

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4.2) [2 pt.] A sample is the proportion of the universe that is selected for analysis.

O True

O False

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4.3) (2 pt.] If a set of data is perfectly symmetrical, the mean must be identical to median.
O True
O False
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4.4) [2 pt.] The Z score can never be negative.
O True
O False
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4.5) (2 pt.] In a Poisson distribution, the mean and variance are equal.
O True
O False
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5.1) [2 pt.] The process of using data collected from a small group to reach conclusions about a large group is called
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O Statistical inference.
O Descriptive statistics.
O Operational definition.
ODCOVA framework.
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5.2) (2 pt.] Suppose we have the following house price data in the excel sheet. What is the function that does NOT calculate the sample mean of the house price data?

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O =SUM(B2:B7)/COUNT(B2:37)

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5.3) [2 pt.] Researchers are concerned that the weight of the average American school child is increasing implying, among other things, that children’s clothing should be

manufactured and marketed in larger sizes. If X is the weight of school children sampled in a nationwide study without rounding, then X is an example of

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a table of random numbers.

O a continuous variable.

O a discrete variable.

O a categorical variable.

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5.3) [2 pt.] Researchers are concerned that the weight of the average American school child is increasing implying, among other things, that children's clothing should be
manufactured and marketed in larger sizes. If X is the weight of school children sampled in a nationwide study without rounding, then X is an example of
O a table of random numbers.
a continuous variable.
a discrete variable.
O
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a categorical variable.
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5.4) [2 pt.] The collection of all possible events is called
O a joint probability.
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a distribution.
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a sample space.
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5.5) [2 pt.] The covariance
O Can be any real value
O Must be non-negative
O Must be between -1 and +1
O Must be positive
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