8.6 The Normal Distribution

1. If data are normally distributed with mean 8 and standard deviation 2, what percent of the data falls between 4 and 12?
2. If data are normally distributed with mean 25 and standard deviation 5, what percent of the data falls between 20 and 30?
3. If data are normally distributed with mean 200 and standard deviation 15, what percent of the data falls between 155 and 245?

1. If data are distributed normally with mean 100 and standard deviation 20, between what two values will 68% of the data fall?
2. If data are distributed normally with mean 0 and standard deviation 15, between what two values will 95% of the data fall?
3. If data are distributed normally with mean 14 and standard deviation 2, between what two values will 99.7% of the data fall?

Suppose we have data that are normally distributed with mean 50 and standard deviation 6. Compute the standardized scores (rounded to three decimal places) for these data values:

1. 52
2. 40
3. 68

Suppose we have data that are normally distributed with mean 10 and standard deviation 2. Convert the following standardized scores into data values.

1. 1.4
2. −0.9
3. 3.5

Suppose we have data that are normally distributed with mean 28 and standard deviation 4. At what percentile do each of the following data values fall?

1. 30
2. 23
3. 35

Suppose we have data that are normally distributed with mean 47 and standard deviation 9. Find the data values (rounded to the nearest tenth) corresponding to these percentiles:

1. 75th (that’s the third quartile)
2. 12th
3. 90th