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Chapter 4: Q. AP1.6 (page 293)

The figure shows a Normal density curve. Which of the following gives the best estimates for the mean and standard deviation of this Normal distribution?

a. μ=200,σ=50

b. μ=200,σ=25

c.μ=225,σ=50

d.μ=225,σ=25

e.μ=225,σ=275

Short Answer

Expert verified

Option (c) μ=225,σ=50best estimated for the mean and standard deviation of this Normal distribution.

Step by step solution

01

Given Information

We have been given a Normal density curve.

02

Explanation

The normal distribution's mean is found near the apex of the normal density curve. We see that the horizontal axis peak is roughly at 225, thus we estimate the mean to be around 225.

μ=225

The standard deviation is the distance from an inflection point (point where the curve is roughly a straight line) of the Normal density curve to the mean μ=225. We note that the inflection point corresponds roughly with 275on the horizontal axis and thus the standard deviation σis the difference between 275and the mean μ=225

σ=275-μ=275-225=50

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