The lifetimes of batteries produced by the juicy battery company are normally distributed with a mean of 100 hours and a standard deviation of 10 hours. find the number of hours where at least 90% of the batteries will continue to operate at.

The z-score associated with 90% is:

P (0.9) = 1.28

sup[pose the number of hours whereby at least 90% of the batteries will continue to operate is x.

the z-score is given by:

z = (x-μ) / σ

where:

μ is the mean

σ is the standard deviation

substituting the values we shall have:

1.28 = (x-100) / 10

solving for x we get:

x=112.8 hours