Question

A manufacturer produces $25$-pound lifting weights. The lowest actual weight is $24$pounds, and the highest is $26$pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of $100$weights is taken.

Draw the graph from Exercise $7.39$

Short answer

The probability that the mean actual weight for the $100$weights is greater than $25.2$is given by the following graph

Step-by-step solution

Given Information

We have $25$-pound lifting weights. The lowest actual weight is $24$pounds, and the highest is $26$ pounds. The distribution of weights is uniform.

Explanation

From Example, $7.39$we know:

The mean of the uniform distribution is

${\mu }_X=\frac{a+b}{2}$

$=\frac{24+26}{2}$

$=25$

The standard deviation is

${\sigma }_x=\sqrt{\frac{(b-a{)}^2}{12}}$

$=\sqrt{\frac{(26-24{)}^2}{12}}$

$=\sqrt{\frac{4}{12}}$

$=0.5774$

The distribution of the mean weight of $100,25$-pounds is

$\overline{X}~N\left({\mu }_X,{\sigma }_X/\sqrt{n}\right)$

$\overline{X}~N(25,0.0577)$

The shaded graph is given below: