Question

The Philips manufactures electric bulbs that have a length of life that is normally distributed with mean equal to 850 hours and standard deviation of 40 hours. Find the probability that a bulb burns between 780 and 834 hours.​

Answer 1

The answer is below

Step-by-step explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by the formula:

`z=(x-\mu)/(\sigma) \\\\where\ x\ is\ the\ raw\ score,\mu\ is\ the \ mean\ and\ \sigma\ is\ the\ standard\ deviation.\\\\Given\ that:\\\\mean(\mu)=850\ hours,\ standard\ deviation(\sigma)=40\ hours`

For x > 780 hours:

`z=(780-850)/(40) \\\\z=-1.75`

For x < 834 hours:

`z=(834-850)/(40) \\\\z=-0.4`

From the normal distribution table, P(780 < x < 834) = P(-1.75 < z < -0.4) = P(z < -0.4) - P(z < -1.75) = 0.3446 - 0.0401 = 0.3045 = 30.45%