Section S.5 – Practice Problems
1. A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?
2. In a normal distribution, what percentage of observations will lie to the left of the mean?
3. Suppose a normal distribution has a mean of six and a standard deviation of 1.5. Draw the associated normal distribution curve, labeling the axis appropriately.
4. Suppose a normal distribution has a mean of 45 and a standard deviation of 10. Draw the associated normal distribution curve, labeling the axis appropriately.
5. Suppose a normal distribution has a mean of -5 and a standard deviation of 2. Draw the associated normal distribution curve, labeling the axis appropriately.
6. Two normal distributions have the same means, but different standard deviations. Distribution A has a standard deviation of 10, and Distribution B has a standard deviation of 15. Which curve has wider spread along the horizontal axis? Why?
7. About what percent of x values from a normal distribution lie within one standard deviation (left and right) of the mean of that distribution?
8. About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?
9. About what percent of x values lie between the second and third standard deviations (both sides)?
10. Suppose the variable X is normally distributed with mean 15 and standard deviation 3. Between what x values does 68% of the data lie? Note: The range of x values is centered at the mean of the distribution.
11. Suppose X is normally distributed with mean -3 and standard deviation 1. Between what x values does 95% of the data lie? Note: The range of x values is centered at the mean of the distribution.
12. About what percent of x values lie between the mean and three standard deviations?
13. About what percent of x values lie between the mean and one standard deviation?
14. About what percent of x values lie between the first and second standard deviations from the mean (both sides)?
15. About what percent of x values lie between the first and third standard deviations (both sides)?
16. The scores on a test are normally distributed with a mean of 120 and a standard deviation of 25. Find the score that is:
b. 95%
c. 99.7%
a. Between 8.97 and 9.27
b. between 8.82 and 9.42
c. between 9.12 and 9.27
d. Between 9.12 and 9.42
e. between 8.82 and 9.12
f. between 8.97 and 9.12
g. Between 8.67 and 9.12
h. between 9.12 and 9.57
i. more than 9.27
j. more than 9.42
k. less than 8.82
l. less than 8.97
20. The resting heart rates for a sample of individuals are normally distributed with a mean of 70 BPM (beats per minute) and a standard deviation of 15 BPM. Use the 68-95-99.7 rule to find the percentage of heart rates in each of the following categories.
a. less than 85
b. less than 40
c. greater than 115
d. less than 100
e. greater than 85
f. greater than 55
g. greater than 40
h. between 55 and 85
i. less than 55
j. between 70 and 100
k. greater than 25
21. In a foreign country, beginning teachers’ salaries have a mean of $55,140 with a standard deviation of $4610. Use the 68-95-99.7 rule to figure the percentage of salaries
a. between $45,920 and $64,360
b. between $50,530 and $59,750
c. between $45,920 and $55,140
d. between $50,530 and $55,140
e. above $59,750f. above $64,360
f. below $45,920h. below $50,530
g. above $68,970j. below $41,310
