Normal Proportions and Values
The weights of newborn babies are normally distributed with a mean of 7.5 pounds and a standard deviation of 1.2 pounds. What proportion of newborn babies weigh less than 6 pounds?
.10565
A normal distribution has a mean of 8 and a standard deviation of 2. What value is 2 standard deviations above the mean?
12
What is the mean of a standard normal distribution?
Zero
Heights are distributed according to N(67,3). What z-score corresponds to a height of 73 inches?
z=2
For a normal distribution, find the z-score that separates the highest 30% from the rest of the distribution.
z=0.52
The weights of newborn babies are normally distributed with a mean of 7.5 pounds and a standard deviation of 1.2 pounds. What proportion of newborn babies weigh more than 8 pounds?
.33846
A normal distribution has a mean of 15 and a standard deviation of 3. What value is 3 standard deviations below the mean?
6
What is the standard deviation of a standard normal distribution?
One
A normal distribution has a mean of 7 and a standard deviation of 2.5. What z–score corresponds to a raw score of 10 for this distribution?
z=1.2
For a normal distribution, find the z-score for the 40th percentile?
z=-0.25
The weights of newborn babies are normally distributed with a mean of 7.5 pounds and a standard deviation of 1.2 pounds. What proportion of newborn babies weigh between 6 and 7 pounds?
0.23281
A normal distribution has a mean of 10 and a standard deviation of 1. Approximately what percentage of data points that fall between the values of 8 and 12?
95%
How much area is to the left of the z-score 1.05?
.85314
A normal distribution has a mean of 60 and a standard deviation of 3.9. What z-score corresponds to the value 50?
z=-2.56
What is the z-score for the third quartile?
z=-0.67
The weights of newborn babies are normally distributed with a mean of 7.5 pounds and a standard deviation of 1.2 pounds. How heavy is a baby at the 90th percentile?
9.04 pounds
A normal distribution has a mean of 24 and a standard deviation of 6. 68% of the values of this distribution fall between what two data values?
18 and 30
How much area is to the right of the z-score -1.93?
0.97320
Charlie took the MCAT (a test to help him get into medical school) and his z-score was 3.2. Interpret this z-score.
Charlie scored 3.2 standard deviations above the mean MCAT score.
What is the range of z-scores for the middle 80% of observations?
-1.28<z<1.28
The weights of newborn babies are normally distributed with a mean of 7.5 pounds and a standard deviation of 1.2 pounds.What is the weight of a baby at the 35th percentile?
7.04 pounds
A normal distribution has a mean of 100 and a standard deviation of 10. Approximately what percentage of data values will fall between the values of 70 and 90?
15.85%
How much area is between the z-scores -0.84 and 1.28?
0.79946
A normal distribution has a mean of 75 and a standard deviation of 5. What value has a z-score of -1.5?
67.5
The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of 35 and a standard deviation of 6. Assuming these raw scores form a normal distribution, what test score represents the 65th percentile?
37.31