Question

A well-known company produces a cellphone whose average lifetime has been estimated to be 4 years.

1. What is the probability that phones lasts less than 5 years?

1. 0.2212                      b) 0.2865                 c) 0.6065             d) 0.7135

2. What is the probability that phones break after 2 years?

1. 0.2212                      b) 0.2865                 c) 0.6065             d) 0.3628

3. Out of 100 phones sold, what is the probability that at most 50 of those will break after 2 years?

1. 0.0188                      b) 0.2865                 c) 0.3483             d) 0.3628

Answer 1

We are given the average lifetime here as 4 years, which means that the distribution of the lifetime here is obtained as:

as parameter for exponential distribution is reciprocal of its mean.

a) The probability that phones lasts less than 5 years is computed here as:

b) The probability that the phone break after 2 years is computed here as:

c) Out of 100 phones the number of phones which break after 2 years can be modelled here as:

As np = 100*0.6065 >= 5, therefore we can approximate this using normal distribution as:

The probability here is computed as:

P( X <= 50)

Applying the continuity correction, we get here:

P(X < 50.5)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.0188 is the required probability here.