Question

An electronic product takes an average of 8 hours to move through an assembly line. If the standard deviation of 0.4 hours, what is the probability that an item will take between 8.4 and 9.1 hours to move through the assembly line?

Answer 1

Answer: 0.1557

Explanation:

Given : Mean :
`\mu=\ 8`

Standard deviation :
`\sigma= 0.4`

The formula to calculate the z-score :-

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

Let the random variable x (number of hours) is normally distributed .

For x= 8.4

`z=(8.4-8)/(0.4)=1`

For x= 9.1

`z=(9.1-8)/(0.4)=2.75`

The p-value =
`P(8.4<x<9.1)=P(1<z<2.75)`

`=P(z<2.75)-P(z<1)= 0.9970202-0.8413447\\\\=0.1556755\approx0.1557`