Empirical Rule
The percentage of data that falls within one standard deviation of the mean.
68%
The z-score corresponding to an SAT score of 630 when the mean score is 500 and the standard deviation is 100.
z=1.3
The probability of randomly selecting a member of a normally distributed population with a value less than the mean of the population.
.5
The symbol used to represent standard deviation.
What is sigma (lower case)
The percent of data that is within 2 standard deviations of the mean.
95%
The sign of the z-score of any data point that falls BELOW the mean.
negative.
US men in the age group of 20-29 have heights that are normally distributed with a mean of 69.6 inches and a standard deviation of 3.0 inches. This is the probability of randomly selecting a man in this age group whose height is more than 72 inches.
.21
The z score tells you how many of these a data point is from the mean.
standard deviation
The percentage of dat that falls within 3 standard deviations of the mean.
99.7%
The z score of a data point that is equal to the mean of the data.
0
US men in the age group of 20-29 have heights that are normally distributed with a mean of 69.6 inches and a standard deviation of 3.0 inches. This is the probability of randomly selecting a man in this age group whose height is between 66 and 72 inches.
.67
The percent of data that lies outside one standard deviation of the mean.
32%
The z score of a data point that is 2.5 standard deviations below the mean of the data.
z=-2.5
The weights of adult male beagles are normally distributed, with a mean of 25 pounds and a standard deviation of 3 pounds. This is the probability of randomly selected an adult male beagle whose weight is less than 23 pounds.
.25
The percentage of data that lies between the mean and one standard deviation above the mean.
34%
If the mean is 50, and the standard deviation is 10, what is the z-score for a value of 78?
z=2.8
The weights of adult male beagles are normally distributed, with a mean of 25 pounds and a standard deviation of 3 pounds. This is the probability of randomly selected an adult male beagle whose weight is less than 22 pounds or greater than 28 pounds.
.32