2.27 Social Insurance Numbers The data reproduced below, show the last digit of
ID: 2973363 • Letter: 2
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2.27 Social Insurance Numbers The data reproduced below, show the last digit of the social insurance number for a group of 70 students. 1 6 9 1 5 9 0 2 8 4 0 7 3 4 2 3 5 8 4 2 3 2 0 0 2 1 2 7 7 4 0 0 9 9 5 3 8 4 7 4 6 6 9 0 2 6 2 9 5 8 5 1 7 7 7 8 7 5 1 8 3 4 1 9 3 8 6 6 6 6 a. You found in Exercise 1. 70 that the distribution of this data was relatively ''flat," with each different value from 0 to 9 occurring wi1h nearly equal frequency. Using this fact, what would be your best estimate for 1he mean of the data set? b. Use the range approximation to guess the value of s for this set. c. Use your calculator to find the actual values of x and s. Compare with your estimates in parts a and b. 2.28 Social Insurance Numbers, continued Refer to the data set in Exercise 2.27. a. Find the percentage of measurements in the intervals x -'- s, x -'- 2s, and x -'- 3s. b. How do the percentages obtained in part a compare with those given by the Empirical Rule? Should they be approximately the same? Explain.Explanation / Answer
mean=4.523 value of s=.54 percentage=87.30% they are nearly same but equal Definition of 'Empirical Rule' A statistical rule stating that for a normal distribution, almost all data will fall within three standard deviations of the mean. Broken down, the empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the mean.
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