Reference no: EM13332766

Please solve Prob 2 (attached) and expand with work:
2) The time (in hours) a customer spends in a particular store is an exponential random variable T, with E[T] = ½
The time spent in the store by one customer is independent of the 2 number of other customers and their time spent in the store.
(a) What is the probability that a customer will spend more than 1 hour in the store?
(b) If 5 customers enter the store at the same time, what is the probability that the number of them that remain in the store 1 hour later is 2 or more?
Solution
Given T follow exp( ½ )
P(T > 1) = ∫_1^∞¦?1/2 exp?(-t/2)dt? = exp?(-1/2) / 4 = 0.555
For second part we use binomial distribution to find probability
We have n =5 , x = 2 , p = 0.555

P (X ≥ 2 ) = ∑_(r=2)^5¦5!/(r!*(5-r)!) * (0.55)r*(0.45)n-r
= 0.27 + 0.34 + 0.2 + 0.05 = 0.86