Question

The life expectancy of a typical lightbulb is normally distributed with a mean of 1,975 hours and a standard deviation of 25 hours. What is the probability that a lightbulb will last between 1,950 and 2,050 hours?

A) 0.84
B) 0.77
C) 0.82
D) 0.89

Answer 1

Given:
μ = 1975 hours, the population mean
σ = 25 hours, the population std. deviation

Consider these random variables:
x₁ = 1950 and x₂ = 2050 hours.

Calculate z-cores and look up probabilities from the standard table.
z₁ = (1950 - 1975)/25 = -1
P(z < z₁) = 0.1587

z₂ =(2050 - 1975)/25 = 3
P(z < z₂) = 0.9987

Therefore
P(z₁ < z < z₂) = 0.9987 - 0.1587 = 0.84

Answer: A) 0.84