Question

120 hardness measurements are made on a large slab of steel with an average of Rockwell C value of 39 and a standard deviation of 4.0. What percent of measurements should fall between 35 and 45?

Answer 1

Answer: 77.45 %

Explanation:

We assume that the measurements are normally distributed.

Given : Mean :
`\mu=39`

Standard deviation :
`\sigma=4.0`

Let x be the randomly selected measurement.

Now we calculate z score for the normal distribution as :-

`z=(x-\mu)/(\sigma)`

For x = 35, we have

`z=(35-39)/(4)=-1`

For x = 45, we have

`z=(45-39)/(4)=1.5`

Now, the p-value =
`P(35<x<45)=P(-1<z<1.5)`

`=P(z<1.5)-P(z<-1)\\\\=0.9331927-0.1586553=0.7745374\approx0.7745`

In percent ,
`0.7745*100=77.45\%`

Hence, the percent of measurements should fall between 35 and 45 = 77.45 %