Question

The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. what is the probability that a battery you buy lasts at most 100 hours? standardize the variable. x = 100 is equivalent to z =

Answer 1

We have been given that

mean, $\mu = 128$

standard deviation $\sigma = 16$

$x=100$

Let us evaluate the z score using the below mentioned formula

$z=\frac{x-\mu}{\sigma}$

On substituting the given values, we get

$z=\frac{100-128}{16} \\ \\ z=-1.75$

Thus, the value of z is -1.75.

Now, we find the probability that a battery you buy lasts at most 100 hours.

We will find the value for z= -1.75 using the z score table.

$P(z=-1.75)= .04006$

Hence, the required probability is 0.04006

Answer 2

-1.75 is the answer.