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Chapter 6: Q. 2 (page 385)
A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?
The median of the normal distribution will be
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Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.
a. If X = distance in feet for a fly ball, then X ~ _____(_____,_____)
b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.
A bottle of water contains fluid ounces with a standard deviation of ounces. Define the random variable in words. ____________.
Terri Vogel, an amateur motorcycle racer, averages seconds per mile lap (in a seven-lap race) with a standard deviation of seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.
a. In words, define the random variable .
b. ,
c. Find the percent of her laps that are completed in less than seconds.
d. The fastest of her laps are under
e. The middle of her laps are from seconds to seconds.
Suppose . Between what values does of the data lie? The range of values is centered at the mean of the distribution (i.e., 15).
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?
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