Chapter 6: Q. 32 (page 386)
About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?
Short Answer
Approximately of values lies within two standard deviation.
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Chapter 6: Q. 32 (page 386)
About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?
Approximately of values lies within two standard deviation.
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Use the information in Example 6.10 to answer the following questions.
In China, four-year-olds average three hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is hours and the amount of time spent alone is normally distributed. We randomly select one Chinese four-year-old living in a rural area. We are interested in the amount of time the child spends alone per day.
a. In words, define the random variable
b.
c. Find the probability that the child spends less than one hour per day unsupervised. Sketch the graph, and write the probability statement.
d. What percent of children spend over ten hours per day unsupervised?
e. Seventy percent of the children spend at least how long per day unsupervised?
An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of days and a standard deviation of days. An alleged father was out of the country from to days before the birth of the child, so the pregnancy would have been less than days or more than days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? What is the probability that he could be the father? Calculate the localid="1653472319552" -scores first, and then use those to calculate the probability.
Suppose X ~ N(2, 3). What value of x has a z-score of –0.67?
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
Find the probability that it takes at least eight minutes to find a parking space.
a. 0.0001
b. 0.9270
c. 0.1862
d. 0.0668
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