Question

1. CONTINUOUS PROBABILITY DISTRIBUTION: So you have assumed that the lifetime of an Everglow battery is a normal, random variable with a µ = 400 hrs, σ = 50.
   1. What percent of time will the battery fail before reaching 360 hours?
   2. What percent of time will the battery exceed 400 hours?
   3. What percent of time will the battery exceed 390 hours?
   4. What percent of time will the battery exceed 500 hours?
   5. What percent of time will the battery last between 390 hours and 450 hours?

Answer 1

We know that life of the battery is distributed normally.

Mean= 400 hrs

Standard deviation= 50 hrs

For each of the values, we must find the z-values.

z-value= (value-mean) / standard_deviation

a.

P(lifetime<360) = (360-400) / 50

= -40/50

= -0.8

The required probability can be looked up from a z-distribution table.

The value is 0.2119.

b.

400 is the mean value. Thus, the probability of (lifetime>400) = 0.5000.

c.

P(lifetime>390) = 1- P(lifetime<390)

= 1 - P(Z< (390-400)/ 50)

= 1- P(Z<-0.2)

= 1- 0.4207

= 0.5793

d.

P(lifetime>500) = 1- P(lifetime<500)

= 1 - P(Z< (500-400)/ 50)

= 1- P(Z<2)

= 1- 0.9772

= 0.0228

e.

P(390 < lifetime < 450)

= P(lifetime<450) - P(lifetime<390)

= P(Z<(450-400)/50) - P(Z<(390-400)/50)

= P(Z<1) - P(Z<-0.2)

= 0.8413-0.4207

= 0.4206