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Chapter 6: Q.6.120 (page 283)
Explain how to obtain normal scores from Table III in Appendix when a sample contains equal observations.
If two or more samples have the same amount of observations, the normal score can be calculated by treating them as somewhat different from one another.
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From the paper "Effects of Chronic Nitrate Exposure on Gonad Growth in Green Sea Urchin Strongylocentrotus droebachiensis" by S. Siikavuopio et al., we found that weights of adult green sea urchins are normally distributed with mean and standard deviation .
Part (a): Find the percentage of adult green sea urchins with weights between and .
Part (b): Obtain the percentage of adult green sea urchins with weight above .
Part (c): Determine and interpret the percentile for the weights.
Part (d): Find and interpret the decile for the weights.
The National Center for Health Statistics publishes information about birth rates (per population) in the document National Vital Statistics Report. The following table provides a frequency distribution for birth rates during one year for the states and the District of Columbia
a. Obtain a frequency histogram of these birth-rate data.
b. Based on your histogram, do you think that birth rates for the states and the District of Columbia are approximately normally distributed? Explain your answer.
Briefly, for a normally distributed variable, how do you obtain the percentage of all possible observations that lie within a specified range?
6.31 Waiting for the Train. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in minutes, that John waits for the train is a variable with density curve for , and otherwise.
a. Graph the density curve of this variable.
b. Show that the area under this density curve to the left of any number between 0 and 30 equals .
What percentage of the time does John wait for the train
c. less than 5 minutes?
d. between 10 and 15 minutes?
e. at least 20 minutes?
As reported in Runner's World magazine, the times of the finishers in the New York City -km run are normally distributed with mean minutes and standard deviation 9 minutes.
Part (a): Determine the percentage of finishers who have times between and minutes.
Part (b): Determine the percentage of finishers who have times less than minutes.
Part (c): Obtain and interpret the th percentile for the finishing times.
Part (d): Find and interpret the th decile for the finishing times.
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