Question

The amount of time that a mobile phone will work without having to be recharged is a random variable having the Exponential distribution with mean 2.2 days.

a) Find the probability (to three decimal places) that such a mobile phone will have to be recharged in less than 1 days.

   

b) Suppose a new model of smart phone has probability 0.3288 of needing to be recharged in less than 1 days. We have 17 of these new phones, all put in usage on the same day and working independently of each other.

Use RStudio to find (to three decimal places) the probability that at least 6 of them will have to be recharged in less than 1 days.

Answer 1

Let no. of days that a mobile phone will work without having to be recharged be denoted as T.

Given :- T ~ exp(2.2)

Probability that such a mobile phone will have to be recharged in less than 1 days

Probability of needing to be recharged in less than 1 days = 0.3288

Let no. of phones among the 17 phones that will have to be recharged in less than 1 days be denoted by X.

So clearly; X ~ Binomial(17,0.3288)

Thus required probability = P(X6) = 0.506

This probability is calculated using the following RStudio code :-

s=0
for(i in 6:17)
s=s+choose(17,i)*0.3288^i*(1-0.3288)^(17-i)
s