Question

HWAWEI produceces 6 smartphones every 30 seconds Assume that the probability of production is the same for periods of equal length and that production of one period are indepened of the production in another. (Show all your work)
a) What is the expected number of smartphones that can be produced in 2 min?
[5]
b) What is the probability that 15 smartphones will be produced in 2 min?
[5]
c) What is the probability that 2000 smartphones will be produced in 2 hours?
[7.5]
d) What is the probability that at least 6 will be produced in 1 min?
[5]
e) What is the probability that at most 5 will be produced in 1 min?
[5]
f) What is the probability that more 10 will be produced in 20min?

NB!!!! PLEASE ANSWER E&F ONLY

Answer 1

a)

2 mins =2*60=120 seconds

Let X is a random variable shows the number of cell phones produced in 2 mins. Here X has Poisson distribution with parameter as follow:

So  the expected number of smartphones that can be produced in 2 min is 24.

b)

The probability that 15 smartphones will be produced in 2 min is

Excel function used: "=POISSON(15,24,FALSE)"

c)

2 hours = 2 *60 *60 = 7200 seconds

That is X has Poisson distribution with parameter

The probability that 2000 smartphones will be produced in 2 hours is

Excel function used: "=POISSON(2000,1440,FALSE)"

d)

1 min = 60 seconds

That is X has Poisson distribution with parameter

The probability that at least 6 will be produced in 1 min is

Excel function used: "=1-POISSON(5,12,True)"

e)

The probability that at most 5 will be produced in 1 min is

Excel function used: "=POISSON(5,12,True)"

f)

20 min =20* 60 = 1200 seconds

That is X has Poisson distribution with parameter

The probability that more 10 will be produced in 20 min is

Excel function used: "=1-POISSON(10,240,True)"