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Normal curve Estimate the mean and standard deviation of the Normal density curve below.

Short Answer

Expert verified

Mean of the Normal density curve,

μ≈28

The standard deviation of the Normal density curve,

σ≈5

Step by step solution

01

Given information

02

Calculation

According to 68−95−99.7rule:

In a normal distribution, 68percent of the data lies within 1standard deviation of the mean.

A normal distribution has 95percent of its data within two standard deviations of the mean.

A normal distribution has 99.7%of its data inside 1standard deviation of the mean.

Then

The general Normal density graph is represented as:

The mean is in the middle of the Normal density curve, near the peak of the distribution.

Note that

The peak of the given distribution appears to lie at 28

Thus,

The mean can be estimated as 28

μ=28

Now,

The values one standard deviation from the mean are generally at the inflection points of the distribution (where the curve appears roughly as a straight line and the curvature of the curve gets changed).

Note that

The inflection points appear to be at 23and 33both of which are 5 away from the average of 28

Thus,

The standard deviation can be estimated as 5

σ≈5

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