 # 1. What percent of cases falls between the mean and one standard de...

## Question

1. What percent of cases falls between the mean and one standard deviation above the mean?
2. What percent falls between the mean and -1 to +1 standard deviations from the mean?
3. What percent of scores (if they are normally distributed) will fall between -3 and +3 standard deviations under the normal curve?
4. What does a z score represent?
5. What is the area (%) between a raw score of 113 and 126 in a normal distribution with a mean of 100 and a standard deviation of 10?

For the following three questions, use a distribution with a mean of 47 and a standard deviation of 7.4.
1. What is the probability of a score falling above a raw score of 60?
2. What is the probability of a score falling below a raw score of 39?
3. What is the probability of a score falling between a raw score of 42 and 52?

## Solution Preview

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1. What percent of cases falls between the mean and one standard deviation above the mean?
That´s the area between z=0 and z=1. In a normal distribution table that displays the cumulative F(z), this area will be expressed as F(1)-F(0)=0.8413-0.5000=0.3413. So we have 34.13%.

2. What percent falls between the mean and -1 to +1 standard deviations from the mean?
The question should be rephrased, removing “the mean and”, but anyone understands what the examiner intended: the area between z=-1 and z=+1. That´s F(1)-F(-1)=2(F(1)-F(0))=2x0.3413. SO we get 68.26%....

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