Question 1

Espresso House wants to estimate the proportion of customers who pay with the mobile app. Which sampling method would best ensure a representative sample of all customers?

Accepted Answer

Survey every customer who enters the store for one full day.

Question 2

Suppose the weight of Serlanda Mini bags is normally distributed with mean $$\mu = 55$$ grams and standard deviation $$\sigma = 5$$ grams. What is the probability that a randomly selected bag weighs more than 60 grams?

Accepted Answer

$$P(X \u003e 60) = 0.16$$

Question 3

Which of the following best describes a simple random sample (SRS)?

Accepted Answer

A sample where every possible group of n individuals has an equal chance of being selected.

Question 4

If the average weight of Serlanda Mini bags in a delivery is less than 50 grams, what is the most likely statistical explanation?

Accepted Answer

The sample may not be representative of the population.

Question 5

A company wants to minimize the probability of paying the penalty for underweight bags. If the penalty applies when the average weight of 30 bags is less than 53 grams, what statistical concept should they use to assess risk?

Accepted Answer

Sampling distribution of the sample mean

Question 6

You take a simple random sample (SRS) of 100 customers and find that 25 are under age 25. What is the sample proportion of young customers?

Accepted Answer

$$\hat{p} = \frac{25}{100} = 0.25$$

Question 7

Which of the following is NOT a characteristic of a normal distribution?

Accepted Answer

It is skewed to the right.

Question 8

Suppose you want to estimate the average spending per customer at Espresso House. Which of the following would reduce the margin of error in your estimate?

Accepted Answer

Increase the sample size.

Question 9

If the weights of Serlanda Mini bags are independent and normally distributed, what is the distribution of the average weight of a sample of 30 bags?

Accepted Answer

Normal distribution with mean $$\mu$$ and standard deviation $$\frac{\sigma}{\sqrt{30}}$$

Question 10

A factory produces bags of chips with weights that are normally distributed with mean $$\mu = 55$$ grams and $$\sigma = 5$$ grams. What is the $$z-$$score for a bag weighing 65 grams?

Accepted Answer

$$z = \frac{65 - 55}{5} = 2$$

Question 11

Why is it important to use a random sample when conducting a survey?

Accepted Answer

To ensure the sample is representative of the population.

Question 12

If you summarize the weights of 300 bags and find the mean is 54 grams, what does this number represent?

Accepted Answer

The average weight in the sample.

Question 13

Which command in statistical software would you use to find the proportion of bags weighing at least 55 grams?

Accepted Answer

tabulate above55

Question 14

If the sample mean and population mean are very close, what does this suggest about your sample?

Accepted Answer

The sample is likely representative of the population.

Question 15

A bag of chips weighs 50 grams. If the population mean is 55 grams and $$\sigma = 5$$ grams, what is the $$z-$$score?

Accepted Answer

$$z = \frac{50 - 55}{5} = -1$$

Question 16

Which of the following is a parameter, not a statistic?

Accepted Answer

The mean weight of all bags produced by the factory.

Question 17

If you want to estimate the proportion of bags weighing at least 55 grams in a population, which formula would you use for the sample proportion?

Accepted Answer

$$\hat{p} = \frac{	ext{number of bags } \geq 55}{	ext{total number of bags in sample}}$$

Question 18

Which scenario best illustrates the concept of sampling error?

Accepted Answer

The sample mean differs from the population mean due to random chance.

Question 19

If the weights of bags are independent, what is the expected value of the average weight in a simple random sample?

Accepted Answer

The population mean $$\mu$$

Question 20

Suppose you want to find the probability that the average weight of 30 bags is less than 53 grams, given $$\mu = 55$$ and $$\sigma = 5. $$Which formula would you use?

Accepted Answer

$$z = \frac{53 - 55}{5 / \sqrt{30}}$$

Statistics for Business: Study Notes on Sampling, Probability, and the Normal Distribution

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