The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1600 hours and a standard deviation of 75 hours. What is the probability that a randomly chosen light bulb will last less than 1460 hours, to the nearest thousandth

0.031 = 3.1% probability that a randomly chosen light bulb will last less than 1460 hours.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 1600 hours and a standard deviation of 75 hours.

This means that

What is the probability that a randomly chosen light bulb will last less than 1460 hours?

This is the p-value of Z when X = 1460. So

has a p-value of 0.031.

0.031 = 3.1% probability that a randomly chosen light bulb will last less than 1460 hours.

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation: