Acompany makes batteries with an average life span of 300 hours with a standard deviation of 75 hours. assuming the distribution is approximated by a normal curve fine the probability that the battery will last: (give 4 decimal places for each answer)

1. less than 250 hours

2. between 225 and 375 hours

3. more than 400 hours

1.

2.

3.

Step-by-step explanation:

Given information: Population mean = 300 hours, Standard deviation=75

Let X be the life of battery in hours.

(1) The probability that the battery will last less than 250 hours is

Therefore the probability that the battery will last less than 250 hours is 0.2546.

(2) The probability that the battery will last between 225 and 375 hours is

Therefore the probability that the battery will last between 225 and 375 hours is 0.6826.

(3) The probability that the battery will last more than 400 hours is

Therefore the probability that the battery will last more than 400 hours is 0.0918.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4