Flashcard Z-Scores

Front

What is a z-score?

Back

Front

How do you interpret a positive z-score?

Back

A positive z-score indicates that the data point is above the mean.

Front

How do you interpret a negative z-score?

Back

A negative z-score indicates that the data point is below the mean.

Front

What is the significance of the 75th percentile in relation to z-scores?

Back

The 75th percentile corresponds to a z-score of approximately 0.67, meaning that 75% of the data points are below this value.

Front

If a data set has a mean of 20 and a standard deviation of 3, what is the z-score for a value of 23?

Back

Front

What percentage of students pass a test if the mean score is 42% and the standard deviation is 8%, with a passing score of 50%?

Back

Using the z-score formula, the percentage of students passing is approximately 16%.

Front

How do you calculate the probability of a value falling within a certain range in a normal distribution?

Back

Use the z-score to find the corresponding probabilities from the standard normal distribution table.

Front

What is the mean and standard deviation of the battery life of a computer if it is normally distributed with a mean of 50 hours and a standard deviation of 15 hours?

Back

Mean = 50 hours, Standard Deviation = 15 hours.

Front

What is the probability that the battery life of a computer will be between 50 and 70 hours?

Back

The probability is approximately 0.4087.

Front

If a data set has a mean of 300 and a standard deviation of 40, what value corresponds to a z-score of -2?

Back