The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1300 hours and a standard deviation of 90 hours. What is the probability that a randomly chosen light bulb will last less than 1230 hours, to the nearest thousandth?
To solve this problem, we need to find the z-score of 1230 hours using the formula:
z = (X - μ) / σ
Where:
X = 1230 hours
μ = 1300 hours
σ = 90 hours
z = (1230 - 1300) / 90
z = -70 / 90
z = -0.7778
Next, we use a standard normal distribution table or a calculator to find the probability that a z-score of -0.7778 occurs. The probability of a z-score of -0.7778 or lower is 0.2206.
Therefore, the probability that a randomly chosen light bulb will last less than 1230 hours is 0.2206, or 22.06% when rounded to the nearest thousandth.