Probability and Statistics Quiz

Which of the following scenarios is most likely to be modeled by a Poisson distribution?

• A) The probability of drawing a red card from a deck of cards 10 times.

• B) The number of people entering a store per hour.

• ) The number of times you get heads when flipping a coin 5 times.

• D) The height of students in a classroom.

In a Poisson distribution, what does the parameter λ represent?

• • A) The number of trials in the experiment.

• • B) The probability of success.

• • C) The average rate of occurrences within a given interval.

• • D) The number of failures.

A website receives an average of 6 visits per minute. What is the probability that exactly 8 visits occur in one minute?

• 0.1032

• 0.1231 (correct)

• 0.1698

• 0.0257

A customer service center receives an average of 4 calls per hour. What is the probability that they receive no calls in the next hour?

• 0.0183 (correct)

• 0.0498

• 0.0834

• 0.1005

What is the mean of the standard normal distribution?

• 1

• 0

• -1

• It can vary

Why is a z-score useful in the standard normal distribution?

• It tells you the number of trials in an experiment.

• It always equals the mean.

• It represents the total probability.

• It shows how many standard deviations a value is from the mean.

The weights of apples are normally distributed with a mean of 150 grams and a standard deviation of 10 grams. What is the probability that an apple weighs less than 140 grams?

• 0.1587 (correct)

• 0.3085

• 0.8413

• 0.6915

In a city, the annual rainfall follows a normal distribution with a mean of 40 inches and a standard deviation of 5 inches. What is the probability that the annual rainfall exceeds 45 inches?

• 0.6915

• 0.3085 (correct)

• 0.1587

• 0.8413

What is the probability that a z-score is less than -1.25 in a standard normal distribution?

• 0.1056 (correct)

• 0.2119

• 0.3944

• 0.8944

What percentage of data falls within 2 standard deviations of the mean in a standard normal distribution?

• 95% (correct)

• 68%

• 99.7%

• 84%