Question 1

A pharmaceutical company wants to estimate the average time it takes for a new drug to relieve pain. Which of the following best describes the population and sample in this scenario?

Accepted Answer

The population is all patients who take the new drug; the sample is the subset of patients observed in the study.

Question 2

Which sampling method is most likely to introduce bias if a university surveys only students who attend morning classes to estimate average study hours?

Accepted Answer

Convenience sampling

Question 3

A company records the number of defective products each day for a month. Which type of data is this?

Accepted Answer

Quantitative discrete data

Question 4

Which of the following is NOT a valid reason to use a histogram instead of a bar chart?

Accepted Answer

Histograms are used for categorical data.

Question 5

Given the following data set: 2, 4, 6, 8, 10. What is the mean?

Accepted Answer

$$ \frac{2+4+6+8+10}{5} = 6 $$

Question 6

A data set has the values: 3, 7, 9, 12, 15. What is the median?

Accepted Answer

$$ 9 $$

Question 7

A company measures the heights (in cm) of its employees and finds a standard deviation of 5 cm. What does this value represent?

Accepted Answer

The average difference between each height and the mean height.

Question 8

If the 75th percentile of exam scores is 80, which statement is true?

Accepted Answer

75% of students scored below 80.

Question 9

If the probability of rain tomorrow is 0.3, what is the probability that it does NOT rain?

Accepted Answer

$$ 1 - 0.3 = 0.7 $$

Question 10

A student rolls a fair six-sided die. What is the probability of rolling a 2 or a 4?

Accepted Answer

$$ \frac{2}{6} = \frac{1}{3} $$

Question 11

In a contingency table, which value represents the probability of both events A and B occurring?

Accepted Answer

The cell at the intersection of A and B.

Question 12

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of cars sold by a dealership in a day.

Question 13

A binomial experiment consists of 10 trials with a probability of success $$ p = 0.2 . $$What is the probability of exactly 3 successes?

Accepted Answer

$$ \binom{10}{3} \cdot (0.2)^3$ \cdot (0.8)^7$ $$

Question 14

Which statement about the standard normal distribution is correct?

Accepted Answer

It has a mean of $$ 0 $$ and a standard deviation of $$ 1 .$$

Question 15

A normal distribution has mean $$ \mu = 50 $$ and standard deviation $$ \sigma = 10 . $$What is the $$ z -$$score for $$ x = 70 $$?

Accepted Answer

$$ z = \frac{70 - 50}{10} = 2 $$

Question 16

According to the Central Limit Theorem, what happens to the sampling distribution of the sample mean as the sample size increases?

Accepted Answer

It approaches a normal distribution, regardless of the population distribution.

Question 17

A random sample of 100 voters is taken from a city where 60% support a new policy. What is the expected value of the sample proportion?

Accepted Answer

$$ 0.60 $$

Question 18

A company wants to know if the average salary of its employees is different from the industry average. Which statistical concept allows them to use a sample mean to make inferences about the population mean?

Accepted Answer

Sampling distribution of the sample mean

Question 19

A researcher uses Excel to calculate the probability that a binomial random variable with $$ n = 5 $$ and $$ p = 0.4 $$ equals 2. Which Excel function should they use?

Accepted Answer

BINOM.DIST(2, 5, 0.4, FALSE)

MAT 137 Midterm Study Guide: Chapters 1–5 (Business Statistics)

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