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Chapter 6: Q.13 (page 385)
What is the z-score of x= –, if it is standard deviations to the right of the mean?
Thescore will be
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Height and weight are two measurements used to track a child’s development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender. In 2009, weights for all cm girls in the reference population had a mean kg and standard deviation . Weights are normally distributed. . Calculate the z-scores that correspond to the following weights and interpret them.
a. 11 kg
b. 7.9 kg
c. 12.2 kg
Find the probability that x is between one and four.
In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is ____ standard deviations to the ____ (right or left) of the mean.
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.
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 1.5 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 X.
b. X ~ _____(_____,_____)
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 the children spend over ten hours per day unsupervised?
e. Seventy percent of the children spend at least how long per day unsupervised?
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