Question 1

Which of the following best describes a probability distribution?

Accepted Answer

A table or function that assigns probabilities to all possible outcomes of a random variable such that the probabilities sum (or integrate) to 1.

Question 2

Suppose the number of stars given to a book on Amazon.ca by a randomly selected reviewer is modeled by the following probability distribution: 1 star (0.033), 2 stars (0.020), 3 stars (0.035), 4 stars (0.156), 5 stars (0.756). What type of random variable is this?

Accepted Answer

Discrete random variable

Question 3

A researcher measures the diameter of cells in a culture. Which type of probability distribution is most appropriate for modeling these measurements?

Accepted Answer

Continuous probability distribution

Question 4

The probability that a newborn grizzly bear cub weighs less than 625 grams, given $$N(650, 20)$$, is found by first calculating the z-score. What is the formula for the z-score?

Accepted Answer

$$ z = \frac{x - \mu}{\sigma} $$

Question 5

In a biotechnology lab, the protein yield per batch follows $$N(50, 5). $$What percentage of batches produce between 45 mg and 55 mg of protein?

Accepted Answer

About 68%, according to the Empirical Rule

Question 6

Which of the following is NOT a condition for using the Central Limit Theorem for sample proportions?

Accepted Answer

The sample must be drawn from a normally distributed population.

Question 7

A poll of 596 Canadians found that 56% would look for another job if required to return to the office full time. In this context, what is the sample statistic?

Accepted Answer

56%

Question 8

Which formula gives the standard deviation of the sampling distribution of a sample proportion?

Accepted Answer

$$ SD = \sqrt{\frac{p(1-p)}{n}} $$

Question 9

A genetic transformation experiment has a 60% success rate. If 15 colonies are tested, what is the probability that exactly 8 express the gene? Which formula should be used?

Accepted Answer

$$ b(n, p, x) = \binom{n}{x} p^x (1-p)^{n-x} $$

Question 10

Which of the following best describes sampling bias?

Accepted Answer

A systematic tendency for a sample to differ from the population in a specific way.

Question 11

A bus arrives every 12 minutes. If the probability density function for waiting time is given, how do you find the probability of waiting between 4 and 10 minutes?

Accepted Answer

Calculate the area under the curve between 4 and 10 minutes.

Question 12

Which of the following is true about the normal distribution?

Accepted Answer

It is symmetric and unimodal.

Question 13

If a sample statistic is both accurate and precise, what does this mean?

Accepted Answer

It is close to the true population parameter and consistent across repeated samples.

Question 14

Which of the following is an example of measurement bias?

Accepted Answer

A scale that consistently reads 2 kg heavier than the true weight.

Question 15

According to the Central Limit Theorem, as the sample size increases, the sampling distribution of the sample mean:

Accepted Answer

Becomes approximately normal, regardless of the population distribution.

Question 16

If the probability that a newborn grizzly bear cub weighs less than 625 grams is 0.1056, what is the probability that a cub weighs more than 625 grams?

Accepted Answer

$$ 1 - 0.1056 = 0.8944 $$

Question 17

A sample of 200 bacterial cultures shows 34% are antibiotic-resistant. What is the standard deviation of the sample proportion?

Accepted Answer

$$ \sqrt{\frac{0.34 	imes 0.66}{200}} = 0.0335 $$

Question 18

Which of the following is a key difference between discrete and continuous probability distributions?

Accepted Answer

Discrete distributions assign probabilities to specific values; continuous distributions assign probabilities to intervals via area under the curve.

Probability Distributions, The Normal and Binomial Models, and Statistical Inference

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