Chapter 2.2, Problem 50E

To determine

Mean and standard deviation of the Normal density curve.

Answer to Problem 50E

Mean of the Normal density curve,

  $\mu \approx 28$

Standard deviation of the Normal density curve,

  $\sigma \approx 5$

Explanation of Solution

Given:

  

According to 68 − 95 − 99.7 rule:

68% of the data of a normal distribution lies with 1 standard deviation from the mean.

95% of the data of a normal distribution lies with 2 standard deviation from the mean.

99.7% of the data of a normal distribution lies with 1 standard deviation from the mean.

Then

The general Normal density graph is represented as:

  

The mean lies at the peak of the distribution and in the middle of Normal density curve.

Note that

The peak of given distribution appears to lie at 28.

Thus,

The mean can be estimated as 28.

  $\mu =28$

Now,

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

Note that

Inflection points appear to lie at 23 and 33, which are both 5 away from the mean of 28.

Thus,

The standard deviation can be estimated as 5.

  $\sigma \approx 5$