Question

An average pen manufactured by the F&M Corporation lasts 400 days with a standard deviation of 40 days.

Assuming that pen life is normally distributed, what is the probability that such a pen will last at least 440
days?

Answer 1

The probability that the pen will last at least 440 days is 0.1587

Explanation:

Given that

Mean = μ = 400 days

SD = σ = 40 days

Now we have to find the probability of a data point X = 440

For that first of all we have to find the z-score of the value

z-score is found using the formula

`z-score = (x-Mean)/(SD)`

Putting the values of x, mean and SD we will get,

`z = (440-400)/(40) = (40)/(40) = 1`

At least 440 means that either 440 or greater than this, hence, we have to find area to the right of z=1

For that

`P(z<1) = 0.8413\\P(z>1) = 1-P(z<1) = 1-0.8413 = 0.1587`

Hence,

The probability that the pen will last at least 440 days is 0.1587