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LSP 121 -- Activity 4

Areas under the Normal Histogram

Look up the percentages or percentiles in this standard normal table. (For example, the 93rd percentile is the x-value, such that 93% of the values are less than equal to that x-value.)

1. A set of IQ scores has a mean of 100 with a standard deviation of 15.
   1. What proportion of scores are 115 or less?

   2. What proportion of scores are 125 or less?

   3. What is the 94th percentile? You will need to work backwards from the percentage to the IQ score.

   4. What is the 6th percentile?

2. The heights of american women, ages 18 to 24 are normally distributed with mean 65.5 and SD 2.5.
   1. What percentage of women are 5'8" or shorter?

   2. What percentage of women are 5'8" or taller?

   3. What percentage of women are 6' or shorter?

   4. What percentage of women are 6' or taller?

   5. What is the 90th percentile for height?

   6. What is the 99th percentile for height?

   7. What is the 10th percentile for height?

3. When a woman learns she is pregnant, her doctor usually calculates a "due date" for the baby. The due date represents the date on which the baby will be born if her pregnancy lasts the mean length for all pregnancies. Actual lengths of pregnancy terms turn out to be nearly normally distributed about this due date (the mean) with a standard deviation of 15 days.
   1. About what percentage of births occur sooner then 10 days after the due date? (The due date is "day 0.")

   2. About what percentage of births occur more than 20 days before the due date?

   3. About what percentage of births occur within 15 days of the due date?

   4. About what percentage of births occur within 1 month of the due date?