Uniform and Normal Distributions

Front

What is a continuous random variable?

Back

A random variable that can take on any value within a given interval.

Front

The waiting time for the train that leaves every 30 minutes is uniformly distributed from 0 to 30 minutes. Find the probability that a person arriving at a random time will wait between 10 and 15 minutes.

Back

1/6

Front

What is the expected value (mean) of a continuous uniform random variable?

Back

(a + b) / 2

Front

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. About what percent of the products last between 12 and 15 days?

Back

34%

Front

The mean GPA of students in a course at UGA is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between 2.9 and 3.8?

Back

81.5%

Front

What is a uniform distribution?

Back

A distribution where all outcomes are equally likely within a given range.

Front

What is the probability density function (PDF) of a continuous uniform distribution?

Back

f(x) = 1/(b-a) for a ≤ x ≤ b, and 0 otherwise.

Front

What is the variance of a continuous uniform distribution?

Back

Variance = (b - a)² / 12.

Front

What is a normal distribution?

Back

A continuous probability distribution characterized by a bell-shaped curve, defined by its mean and standard deviation.

Front

What is the empirical rule in statistics?

Back

Approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.