Review of Probability and Statistics Practice Test

These flashcards cover key concepts in probability and statistics as discussed in the practice test.

What is the range of probabilities for any event?

The probability must fall between zero and one.

If 120 students are 30 or older in a community college of 500 students, how many are younger than 30?

380 students are younger than 30.

How do you calculate the probability of an event occurring?

Probability = rac{ ext{Number of favorable outcomes}}{ ext{Total number of outcomes}}.

In a frequency distribution, if 2,164 students major in mathematics out of 9,313, what is the probability of not majoring in mathematics?

Approximately 0.768.

How do you find the probability that a randomly selected student is a boy in a class with 35 students including 20 boys?

The probability is rac{20}{35} which is approximately 0.571.

What is the probability that a customer did not have a medium level of satisfaction given that there are 700 surveys and 220 had medium satisfaction?

Approximately 0.686.

If the expected waiting times in a table include ranges 12 minutes or more, how do you find the total probability for waiting times of at least 12 minutes?

Count all customers over 12 minutes and divide by the total.

For soft drink preferences, if 30 out of 85 people over 40 drink root beer, what is the probability they drink root beer?

The probability is rac{30}{85} which simplifies to rac{6}{17}.

How would you classify the random variable for number of cups of coffee sold in a cafeteria?

Discrete, because you can count the cups.

In a probability distribution, if all probabilities must sum to one, how do you find a missing probability?

Subtract the sum of known probabilities from 1.

What is the empirical rule regarding standard deviations and data distribution?

68% of data is within 1 standard deviation, 95% within 2, and 99% within 3 standard deviations.

If a normal distribution has a mean of 300 and a standard deviation of 40, what range includes approximately 68% of the data?

Between 260 and 340.

In the context of a z-score, what does it mean if we say a z-score is greater than 0?

It is above the mean of the distribution.

When looking for the probability between two z-scores, how do you compute it?

Use StatCrunch to calculate the area between the two z-scores.

What is the expected value in a probability distribution?

The weighted average of all possible outcomes, calculated as ext{E(X)} = ext{Sum of } X_i imes P(X_i).

How do you determine if the number of goals scored in a soccer game is discrete or continuous?

It is discrete since goals are counted as whole numbers.

If a pie sells for $6 and has a cost of $2.50, how do you calculate expected profit when varying sales?

Calculate the profit for different sales scenarios and find the expected value.

If you have a mean daily revenue of $3400 and a standard deviation of $600, how do you describe the sampling distribution of the sample mean n=100?

Mean remains at $3400 and the standard error = rac{600}{ ext{sqrt}(100)} = 60.

What approach should be taken to find the probability that corn chips' weights exceed a particular mean when sampling?

Adjust using the standard deviation divided by the square root of the sample size.

For a distribution with a mean of 99 years and a standard deviation of 14 years, what is the probability of living between 75 and 115 years?

Use standard normal calculations to find probabilities using StatCrunch.