Prob & Stats HW 37 Review of Unit 4

Front

What percentage of data in a normal distribution falls within one standard deviation of the mean?

Back

Approximately 68% of the data.

Front

What is the mean and standard deviation of the shelf life of a particular dairy product?

Back

Mean: 12 days, Standard Deviation: 3 days.

Front

What percentage of products last between the mean and one standard deviation above the mean in a normal distribution?

Back

34%.

Front

In a normal distribution with a mean of 200 and a standard deviation of 50, what percentage of ratings can be expected to be between 200 and 275?

Back

Approximately 43.31%.

Front

What is the lower quartile in a data set?

Back

The lower quartile (Q1) is the median of the lower half of the data set.

Front

What is the mean and standard deviation of human pregnancies?

Back

Mean: 268 days, Standard Deviation: 15 days.

Front

What percentage of pregnancies last at least 300 days in a normal distribution with a mean of 268 days and a standard deviation of 15 days?

Back

Approximately 1.64%.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, about 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean.

Front

What does it mean if a data set is normally distributed?

Back

It means that the data follows a bell-shaped curve where most of the observations cluster around the central peak.

Front

How do you calculate the z-score for a value in a normal distribution?

Back

Z-score = (X - mean) / standard deviation.