A local municipality installs 2000 electric street lamps in...

Name: a local municipality installs 2000 electric street lamps in a new housing development the life expectancy of these lamps measured in hours follows a normal distribution with a mean of 1000 h 16685
Uploaded: 2024-04-29T09:55:12-08:00
Duration: 5 min 33 s
Channel: Robin Corrigan
Description: a local municipality installs 2000 electric street lamps in a new housing development the life expectancy of these lamps measured in hours follows a normal distribution with a mean of 1000 h 16685

A local municipality installs 2000 electric street lamps in a new housing development. The life expectancy of these lamps, measured in hours, follows a normal distribution with a mean of 1000 hours and a variance of 40 000. Let x = the life expectancy of these lamps c) 10% of the lamps bums less than r hours. Calculate r. What percentile is r? d) 25% of the lamps burns more than hours. Calculate t. What percentile is t?

Transcript

00:01 A batch of 5 ,000 electric lamps has a mean life of 1 ,000 hours and a standard deviation of 75 hours, and we assume that the distribution of the lifespans is normal.

00:15 And we are first asked, how many lamps will fail before 900 hours? so we can find the expected number that fail before 900 hours by calculating the probability that an individual lamp lasts less than 900 hours.

00:38 And then multiplying that by the number of lamps.

00:44 So if this graph represents the normal distribution of the lifespans, 900 is somewhere around here, and the probability that x is less than 900 is equal to the area under the curve to the left of 900.

01:05 So we can solve this probability using excel.

01:08 If we use excel, we start a computation with equals.

01:11 We want to use the normal distribution function.

01:14 We enter 900 for the first argument, argument, then the mean, then standard deviation, and then true for the cumulative argument, to get the probability that the light lasts anything up to 900 hours, hit enter, and we get point 0912 approximately.

01:37 So we multiply that probability by 5000.

01:43 And it comes out to approximately 456.

01:47 So 456 of the lamps will fail before 900 hours.

01:53 And for the second question we want to know how many fail between 950 and 1000 hours.

02:08 So we find this probability and multiply by n.

02:15 So first let's express this probability as a cumulative probability...