1. If scores are normally distributed with a mean of 35 and a standard deviation of 10, what percent of the scores is:

a. greater than 34?
b. smaller than 42?
c. between 28 and 34?

2. What proportion of a normal distribution is within one standard deviation of the mean?
Mean=50,sd=1

(a) What proportion is more than 2.0 standard deviations from the mean?

(b) What proportion is between 1.25 and 2.1 standard deviations above the mean?

3. A test is normally distributed with a mean of 70 and a standard deviation of 8.

(a) What score would be needed to be in the 85th percentile?
(b) What score would be needed to be in the 22nd percentile?

4. Assume a normal distribution with a mean of 70 and a standard deviation of 12. What limits would include the middle 65% of the cases?

5. A normal distribution has a mean of 20 and a standard deviation of 4. Find the Z scores for the following numbers:

6. Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.

a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?

b. What proportion of the vehicles would be going less than 50 mph?

c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?

d. In what way do you think the actual distribution of speeds differs from a normal distribution?
The distribution is skewed to the right because there are some people driving over speed.

7. A variable is normally distributed with a mean of 120 and a standard deviation of 5. One score is randomly sampled. What is the probability it is above 127?

Complete the following from simpleR.

6.2,6.3,6.7 6.8