Z Questions

Constructed response quiz questions (Raz-Plus, Raz-Kids, and Science A-Z) give students the opportunity to type a short-answer response to a question. These questions promote close reading and critical thinking skills, and strengthen the reading-writing connection. The Drugs.com Answers and Support Group system is intended as a way of providing help for people who have questions about drugs or medical conditions.

Use this calculator to compute the z-score of a normal distribution.

Z-score and Probability Converter

Please provide any one value to convert between z-score and probability. This is the equivalent of referencing a z-table.

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Probability between Two Z-scores

Use this calculator to find the probability (area P in the diagram) between two z-scores.

What is z-score?

The z-score, also referred to as standard score, z-value, and normal score, among other things, is a dimensionless quantity that is used to indicate the signed, fractional, number of standard deviations by which an event is above the mean value being measured. Values above the mean have positive z-scores, while values below the mean have negative z-scores.

The z-score can be calculated by subtracting the population mean from the raw score, or data point in question (a test score, height, age, etc.), then dividing the difference by the population standard deviation:

where x is the raw score, μ is the population mean, and σ is the population standard deviation.

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The z-score has numerous applications and can be used to perform a z-test, calculate prediction intervals, process control applications, comparison of scores on different scales, and more.

Z-table

A z-table, also known as a standard normal table or unit normal table, is a table that consists of standardized values that are used to determine the probability that a given statistic is below, above, or between the standard normal distribution.

The table below is a right-tail z-table. Although there are a number of types of z-tables, the right-tail z-table is commonly what is meant when a z-table is referenced. It is used to find the area between z = 0 and any positive value, and reference the area to the right-hand side of the standard deviation curve.

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Z Test Questions

Question 1:

According the the U.S. Department of Education, full-time graduate students receive an average salary of $12,800. The dean of graduate studies at a large state university in PA claims that his graduate students earn more than this. He surveys 46 randomly selected students and finds their average salary is $13,445 with a standard deviation of $1800. With alpha = 0.05, is the dean’s claim correct?

Solution:

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Question 2:

A health researcher read that a 200-pound male can burn an average of 524 calories per hour playing tennis. 37 males were randomly selected and the mean number of calories burned per hour playing squash was 534.8 with a standard deviation of 45.9 calories. Do squash players burn more calories per hour than tennis players? Test with alpha = 0.01.

Solution:

Question 3:

To see if young men ages 8-17 years spend a different amount than the national average of $24.44 per shopping trip to a local mall, the manager surveyed 30 young men. She found that the average amount spent per trip was $23.37 with a standard deviation of $3.70. With alpha = 0.05, can it be concluded that 8-17 years old spend a different amount at the local mall than the national average?

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Solution: