Chapter 2.2, Problem 49E

To determine

Mean and standard deviation of the Normal density curve.

Answer to Problem 49E

Mean of the Normal density curve,

  $\mu \approx 10$

Standard deviation of the Normal density curve,

  $\sigma \approx 1$

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 10.

Thus,

The mean can be estimated as 10.

  $\mu =10$

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 9 and 11, which are both 1 away from the mean of 10.

Thus,

The standard deviation can be estimated as 1.

  $\sigma \approx 1$