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Comparing variation
Calculating Percentiles A data set consists of the 85 ages of women at the time that they won an Oscar in the category of best actress.
a. One of the actresses was 40 years of age, and she was older than 63 of the other actresses at the time that they won Oscars. What is the percentile of the age of 40?
b. One of the actresses was54 years of age, and she was older than 76 of the other actresses at the time that they won Oscars. What is the percentile of the age of 54?
c. One of the actresses was 60 years of age, and she was older than 77 of the other actresses at the time that they won Oscars. What is the percentile of the age of 60?
A simple random sample of 50 adults is obtained, and each person's red blood cell count (in cells per micro-liter) is measured. The sample mean is 5.23. The population standard deviation for red blood cell counts is 0.54.
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A random variable X has the Pareto (α, θ) distribution (where α > 0, θ > 0) if F_X(x) = 1 - (θ/(θ+x))^α for x ≥ 0. For a fixed d > 0, let Y = X-d | X >d. Calculate F_Y(y) and EY.
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The makers of a soft drink want to identify the average age of its consumers. A sample of 16 consumers is taken. The average age in the sample was 22.5 years with a standard deviation of 5 years.
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