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Chapter 2: Q.73 (page 135)
The proportion of observations from a standard Normal distribution with values less than is
(a) .
(b) .
(c) .
(d) .
(e) none of these.
The proportion of observations from a standard Normal distribution with values less than is.
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Use Table A to find the value from the standard Normal distribution that satisfies each of the following conditions. In each case, sketch a standard Normal curve with your value of marked on the axis. Use your calculator or the Normal Curve applet to check your answers.
Working backward
(a) The rd percentile.
(b) % of all observations are greater than .
T2.3. Rainwater was collected in water collectors at different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are and , respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding units to all of the values and then multiplying the result by . The mean and standard deviation of the corrected pH measurements are
(a)
(b)
(c)
(d)
(e)
Comparing bone density Refer to the previous exercise. One of Judy’s friends, Mary, has the bone density in her hip measured using DEXA. Mary is 35 years old. Her bone density is also reported as , but her standardized score is. The mean bone density in the hip for the reference population of -year-old women is .
(a) Whose bones are healthier—Judy’s or Mary’s? Justify your answer.
(b) Calculate the standard deviation of the bone density in Mary’s reference population. How does
this compare with your answer to Exercise 13(b)? Are you surprised?
About what proportion of observations lie between and ?
Measure up Clarence measures the diameter of each tennis ball in a bag with a standard ruler. Unfortunately, he uses the ruler incorrectly so that each of his
measurements is inches too large. Clarence’s data had a mean of inches and a standard deviation of inches. Find the mean and standard deviation of the corrected measurements in centimeters (recall that 1 inch = cm).
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