the amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1300 hours and…
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?\nstatistics calculator
Answer
Explanation:
Step1: Calculate the z - score
The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 1230$ (the value we are interested in), $\mu=1300$ (the mean), and $\sigma = 90$ (the standard deviation). $z=\frac{1230 - 1300}{90}=\frac{-70}{90}\approx - 0.778$
Step2: Find the probability
We want to find $P(X\lt1230)$, which is equivalent to $P(Z\lt - 0.778)$ using the standard normal distribution. Looking up the z - score in the standard normal table (or using a calculator with a normal - distribution function), we find that $P(Z\lt - 0.778)\approx0.218$
Answer:
$0.218$