Question

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

Short answer

Mean of the Normal density curve,

$\mu \approx 28$

The standard deviation of the Normal density curve,

$\sigma \approx 5$

Step-by-step solution

Given information

Calculation

According to the $68-95-99.7$rule:

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

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

A normal distribution has $99.7\%$of its data inside $1$standard 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 $28.$

$\mu =28$

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 $23$ and $33$ both of which are $5$away from the average of $28$

Thus,

The standard deviation can be estimated as $5$

$\sigma \approx 5$