Question

Lithium cellphone batteries for a certain model has a lifetime that follows an exponential distribution with β = 3000 hours of continuous use.

1. What is the probability that a randomly chosen battery would last at least 8 months? (assume 30 days in each month)

1. 0.9920   c. 0.8253   e. 0.1466
2. 0.9197   d. 0.8534

2. What is the probability that a randomly chosen battery lasts between 60 to 8 months?

1. 0.0435   c. 0.0795   e. 0.1466
2. 0.0903   d. 0.1457

3. What would be the lower limit (in months) for the top 10% lifetimes?

1. 8.4   c. 7.3    e. 96
2. 9.1   d. 6.2

Answer 1

Let X be the lifetime of batteries

1. What is the probability that a randomly chosen battery would last at least 8 months? (assume 30 days in each month)

8 months = (8 * 30 * 24 )

= 5760 hrs

( multiplying by 30 gives total number of days and multiplying by 24 gives total number hours)

Atleast 8 months = atleast 5760 hours

a. 0.9920   c. 0.8253   e. 0.1466

b. 0.9197   d. 0.8534

2. What is the probability that a randomly chosen battery lasts between 6 to 8 months?

   months = hrs

=

=

=

a. 0.0435   c. 0.0795   e. 0.1466

b. 0.0903 d. 0.1457

3. What would be the lower limit (in months) for the top 10% lifetimes?

Lower limit means the minimum value. We need to find 'x' such that lifetime is 'x' or more 'x' with a probability of 10%

   hrs

= months

a. 8.4   c. 7.3    e. 9.6

b. 9.1   d. 6.2