The average life of a particular car battery is 40 months. The life of a car battery, measured in...

The average life of a particular car battery is 40 months. The life of a car battery, measured in months, is known to follow an exponential distribution.

• X = the life of a particular car battery, measured in months.• = mean = 40 m = 1/ = 1/40 = 0.025 • X ~ Exp( 1/40 ) or Exp(0.025)• Graph of the probability distribution

• On average, how long would you expect one car battery to last?

= 40 months • On average, how long would you expect 3 car batteries to last, if they are used one after another?

3 car batteries last (3)(40) = 120 months

• Find the probability that one of the car batteries lasts more than 36 months.

P(X > 36) =

1 – e-36*1/40 =

0.5934

• Find the probability that one of the car batteries lasts less than 36 months.

P(X < 36)

• Find the probability that one of the car batteries lasts between 36 and 40 months.•Subtract the area to the right of 40 FROM the area to the right of 36.

P(36 < X < 40) =

e-36/40 – e-40/40 =

0.0387

• Find the 90th percentile. (90% of all batteries last less than this number of months.) •Let k = the 90th%ile

•Area to the LEFT = 0.90

Percentile Formula: k = LN(1 – Area LEFT) = -mLN(1-0.9)/(-1/40) = 92.10 months

• 70% of the batteries last at least how long? • Let k = the 30th percentile (0.30 = Area to the LEFT)

• Use the percentile formula

Percentile Formula: k = LN(1 – Area LEFT) = -mLN(1-0.30)/(-1/40) = 14.27 months