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

Answer:

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

Step-by-step 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

$z-score = \frac{x-Mean}{SD}$

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

$z = \frac{440-400}{40} = \frac{40}{40} = 1$

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