Question

The author's Generac generator produces voltage with a mean of 178.03 volts and standard deviation of 0.08 volt, and the voltages have a bell-shaped distribution A)What is the approximation percentage of voltage amounts is to the left of 178.19 voltsB)what is the approximation percentage of voltage amounts is to the right of 177.95 volts

Answer 1

To answer this question we will use the following formula to compute the z-score:

$\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ where\text{ x is the observed value, }\mu\text{ is the mean and }\sigma\text{ is the standard deviation.} \end{gathered}$

A) The z-score for x=178.19V is:

$z=\frac{178.19V-178.03V}{0.08V}=\frac{0.16V}{0.08V}=2.$

Using tables we get:

$P(z<2)=97.72\%$

B) The z-score of 177.95V is:

$z=\frac{177.95V-178.03V}{0.08V}=\frac{-0.08V}{0.08V}=-1.$

Using tables we get:

$P(z>-1)=84.13\%.$

Answer:

A) 97.72%.

B) 84.13%.