Question

Suppose that the lifetimes of light bulbs are approximately normally​ distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this information, answer the following question.

What proportion of light bulbs will last between 59 and 61 hours? (4 decimals)

What is the probablity that a randomly selected light bulb lasts less than 45 hours? (4 decimals)

Answer 1

Solution :

Given that mean μ = 57, standard deviation σ = 3.5

=> P(59 < x < 61) = P((59 - 57)/3.5 < (x - μ)/σ < (61 - 57)/3.5)

= P(0.5714 < Z < 1.1429)

= P(Z < 1.1429) - P(Z < 0.5714)

= 0.8729 - 0.7157

= 0.1572

=> The proportion of light bulbs will last between 59 and 61 hours is 0.1572

=> P(x < 45) = P((x - μ)/σ < (45 - 57)/3.5)

= P(Z < -3.4286)

= 1 - P(Z < 3.4286)

= 1 - 0.9997

= 0.0003

=> The probability that a randomly selected light bulb lasts less than 45 hours is 0.0003