Chapter 5

1. If scores are normally distributed with a mean of 30 and a standard deviation of 5, what percent of the scores is: (a) greater than 30? (b) greater than 37? (c) between 28 and 34?
   
   
2. (a) What are the mean and standard deviation of the standard normal distribution? (b) What would be the mean and standard deviation of a distribution created by multiplying the standard normal distribution by 10 and then adding 50?
   
   
3. The normal distribution is defined by two parameters. What are they?
   
   
4. (a) What proportion of a normal distribution is within one standard deviation of the mean? (b) What proportion is more than 1.8 standard deviations from the mean? (c) What proportion is between 1 and 1.5 standard deviations above the mean?
   
   
5. A test is normally distributed with a mean of 40 and a standard deviation of 7. (a) What score would be needed to be in the 85th percentile? (b) What score would be needed to be in the 22nd percentile?
   
   
6. Assume a normal distribution with a mean of 90 and a standard deviation of 7. What limits would include the middle 65% of the cases.
   
   
7. For this problem, use the scores in the identical blocks test (second in the dataset "High_School_Sample"). Compute the mean and standard deviation. Then, compute what the 25th and 75th percentile would be if the distribution were normal. Compare the estimates to the actual 25th and 75th percentiles.
   

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