Suppose a brand of light bulbs is normally distributed, with a mean life of 1300 hr and a standard deviation of 50 hr. Find the probability that a light bulb of that brand lasts between 1225 hr and 1365 hr.

Step-by-step explanation:

Since the life of the brand of light bulbs is normally distributed, we would apply the the formula for normal distribution which is expressed as

z = (x - u) / s

Where

x = life of the brand of lightbulbs

u = mean life

s = standard deviation

From the information given,

u = 1300 hrs

s = 50 hrs

We want to find the probability that a light bulb of that brand lasts between 1225 hr and 1365 hr. It is expressed as

P (1225 ≤ x ≤ 1365)

For x = 1225,

z = (1225 - 1300) / 50 = - 1.5

Looking at the normal distribution table, the probability corresponding to the z score is

0.06681

For x = 1365,

z = (1365 - 1300) / 50 = 1.3

Looking at the normal distribution table, the probability corresponding to the z score is

0.9032

Therefore

P (1225 ≤ x ≤ 1365) = 0.9032 - 0.06681 = 0.8364