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The weight X of babies (of a fixed age) is normally distributed with mean μ =...

  1. The weight X of babies (of a fixed age) is normally distributed with mean μ = 212 ounces and standard deviation σ = 25 ounces. Doctors would also be concerned (not necessarily alarmed) if a baby is among the upper 10 percent in weight. Find the cut-off weight u, above which the doctors will be concerned.

  2. The weight X of salmon caught in a river is normally distributed with mean μ = 24 pounds and standard deviation σ = 6 pounds. You can keep those that are among that upper 66 percent in weight. What is the cut-off weight l, above which you can keep the fish?

  3. The height of an adult male in a region is known to be normally dis- tributed with mean of μ = 69 inches and a standard deviation σ = 2.5inches. How high should a doorway be so that 92 percent of adult males can pass through it without having to bend?

  4. The hourly wages X in an industry has a normal distribution with mean $40 and standard deviation $17. What is the 97 percentile of the hourly wage?

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Answer #1

#1.
mean = 212
sd = 25

z-value for top 10%, 1.2816

using central limit theorem
x = 212 + 1.2816*25
x = 244.04

Ans: 244.04 ounces

#2.
mean = 24 and sd = 6

z-value for top 66%, 0.4125

using central limit theorem,
x = 24 + 0.4125*6
x = 26.475

Ans: 26.5 ounces

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