# Statistics

Eric has computed that it takes an average (mean) of 17 minutes with a standard deviation of 3 minutes to drive from home, park the car, and walk to his job. One day it took Eric 21 minutes to get to work. You would use the formula for transforming a raw score in a sample into a z-score to determine how many standard deviations the raw score represents. Since his "score" is 21, you would subtract the mean of 17 from 21 and divide that result (4) by the standard deviation of 3. The z-score of 1.33 tells you that Eric’s time to get to work is 1.33 standard deviations from the mean

Questions
Is the z value positive or negative? Explain why it should be positive or negative.
Another day, it took Eric only 12 minutes to get to work. Using the same formula, determine the z value. Is it positive or negative? Explain why it should be positive or negative.
On a different day, it took Eric 17 minutes to get from home to work. What is the z value? Why should you expect this result even before you did the calculation?
Based on your study of z-scores, explain the three uses of z-scores. How might they each relate to Eric's trip between home and work?
What is the relationship between z-scores and the standard normal curve?

1. 👍 0
2. 👎 0
3. 👁 160
1. Since Z = (score-mean)/SD, scores below the mean will have a negative value, and those above the mean will have a positive value.

Since you did the calculation of the first Z score, you should be able to do the same for the other Z scores.

For a normal distribution, the Z scores express raw scores in terms of SDs from the mean. The proportions cut off are the same for any normal distribution. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to your Z scores.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Statistics

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the point in the

asked by Pacifico on March 19, 2010
2. ### Statistics

John drives to work each morning and the trip takes an average of μ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the

asked by Robbie on October 14, 2012
3. ### statistics

A study of 35 professors showed that the average time they spent creating test questions was 13.5 minutes per question. The standard deviation of the population is 3.8. Which of the following is the 99% confidence interval for the

asked by Holly on March 29, 2012
4. ### Dine

Men spend an average of 29 minutes per day on weekends and holidays exercising and playing sports. They spend an average of 23 minutes per day reading. A random sample of 25 men resulted in a mean of 35 minutes exercising with a

asked by angie on November 10, 2014
1. ### statisticss

The time taken by a man to deliver milk is normally distributed with, mean 12 minutes and standard deviation 2 minutes. He delivers milk everyday estimate the probability that he takes. (a) longer than 17 minutes (b) between 9 and

asked by Heidi on July 8, 2014
2. ### math

The length of Paulo’s lunch break follows a normal distribution with mean μ minutes and standard deviation 5 minutes. On one day in four, on average, his lunch break lasts for more than 52 minutes. Find the value of μ.

asked by sanjay on February 13, 2014
3. ### statistics

John drives to work each morning and the trip takes an average of  = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of  = 5 minutes. For a randomly selected morning, what is

asked by karla on April 17, 2011
4. ### Statistics

The average time a visitor spends at the Renzie Park Art Exhibit is 62 minutes. The standard deviation is 12 minutes. If a visitor is selected at random, find the probability that he or she will spend: A)At least 82 minutes at the

asked by John on October 22, 2010
1. ### Statistics

A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off

asked by Alisha on July 11, 2012
2. ### math 540

suppose it takes a college student an average of 5 minutes to find a parking space on the schools parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What time is exceeded by

asked by renee on November 12, 2013
3. ### Statistics

Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it

asked by Lola on May 9, 2019
4. ### Statistics

the average length of time for students to register for fall classes at a certain college has been 50 minutes. a new registration procedure using modern computing machine is being tried. if a random sample of 12 students had an

asked by Jacy on March 10, 2011