The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1200 hours and a standard deviation of 65 hours. What is the probability that a randomly chosen light bulb will last between 1220 hours and 1350 hours, to the nearest thousandth?
To find the probability that a randomly chosen light bulb will last between 1220 hours and 1350 hours, we need to calculate the z-scores for both values and then find the area under the normal curve between those z-scores.
First, we calculate the z-scores:
z1 = (1220 - 1200) / 65 = 0.3077
z2 = (1350 - 1200) / 65 = 2.3077
Next, we use a standard normal distribution table or a calculator to find the area under the curve between z1 and z2:
P(0.3077 < Z < 2.3077) = 0.4884
Therefore, the probability that a randomly chosen light bulb will last between 1220 hours and 1350 hours is approximately 0.4884 or 48.84%.