PROCEDURE 6.2 To Determine the Observations Corresponding to a Specified Percent

Question

PROCEDURE 6.2 To Determine the Observations Corresponding to a Specified Percentage or Probability for a Normally Distributed Variable Step 1 Sketch the normal curve associated with the variable. Step 2 Shade the region of interest. Step 3 Use Table II to determine the z-score(s) delimiting the region found in Step 2. Step 4 Find the r-value(s) having the 2-score(s) found in Step 3. Note: To find eachx value in Step 4 from its z-score in Step 3, use the formola The A. C. Nielsen Company reported in the Nielsen Report on Television that the mean weekly television viewing time for children aged 2-6 years is 24.85 hours. Assume that the weekly televsion viewing times of such children are normally distributed with a standard deviation of 6.23 hours and apply the empirical rule to fill in the blanks. Round Answers to 2 decimal places. Xxx and a. Approximately 68% of all such children watch between hours of TV per week. and b. Approximately 95% of all such children watch between hours of TV per week. and C. Approximately 99.7% of all such children watch between hours of TV per week.

Explanation / Answer

mu = 24.85; sigma = 6.23

(a) mu - sigma = 18.62
mu + sigma = 31.08
18.62 and 31.08 hours of TV.

(b) mu - (2 * sigma) = 12.39
mu + (2 * sigma) = 37.31
12.39 and 37.31 hours of TV.

(c) mu - (3 * sigma) = 6.16
mu + (3 * sigma) = 43.54
6.16 and 43.54 hours of TV.

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