Question

Find the area from $\mathbf{800}$to$\mathbf{1000}$hours.

Short answer

The area under the Gaussian curve of bulbs expected to have a lifetime from 800 to 1000 hours is$0.6342$.

Step-by-step solution

Gaussian curve

Gaussian curve:

A Gaussian curve is defined as a normalized frequency distribution that is symmetrical about the line of zero error

Solve for the area under Gaussian curve of bulbs

Use the Gaussian curve from Figure 4-1.

Calculate the bulbs expected to have a lifetime between 800 to 1000 hours by calculating the area under the Gaussian curve.

From figure 4-1, we know that the mean is,$\left(\overline{\mathrm{X}}\right)=845.2$and the standard deviation is,$\left(s\right)=94.2.$

Now, calculate the fraction of the area of the Gaussian curve between$\mathrm{x}=800$and$\mathrm{x}=1000\mathrm{h}.$

The required area is calculated using the function NORMDIST in excel sheet. This gives the area of the curve from$-\infty$to a specified point,$\mathrm{x}.$

In the below figure 1below, the shaded portion distinguishes the area from $-\infty$to 800 and$-\infty$to 1000.

Figure 1

The difference between these two areas gives the area from 800 to $1000\mathrm{h}.$:

The area from 8 $1000=(\mathrm{area}\mathrm{from}-\infty \mathrm{to}1000)-(\mathrm{area}\mathrm{from}800).$

Figure 2

From the calculations using the function NORMDIST in excel sheet, the area between 800 to 1000 hour is found to be$0.6342.$