Question

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. $\mu =200,\sigma =50$

b. $\mu =200,\sigma =25$

c.$\mu =225,\sigma =50$

d.$\mu =225,\sigma =25$

e.$\mu =225,\sigma =275$

Short answer

Option (c) $\mu =225,\sigma =50$best estimated for the mean and standard deviation of this Normal distribution.

Step-by-step solution

Given Information

We have been given a Normal density curve.

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 $225$.

$\mu =225$

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 $\mu =225$. We note that the inflection point corresponds roughly with $275$on the horizontal axis and thus the standard deviation $\sigma$is the difference between $275$and the mean $\mu =225$

$\sigma =275-\mu =275-225=50$