Question

1. ****NEED TO KNOW HOW PROBLEM IS SET UP IN EXCEL***
2. During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.
   1. Clearly state what the random variable in this problem is?
   2. What is an appropriate distribution to be used for this problem and why?
   3. What is the expected number of calls in one hour?
   4. What is the probability of receiving three calls in five minutes?
   5. What is the probability of receiving NO calls in a 10-minute period?
   6. What is the probability of receiving more than five calls in a 10-minute period?
   7. What is the probability of receiving less than seven calls in 15-minutes?
   8. What is the probability of receiving at least three but no more than 10 calls in 12 minutes?

Answer 1

a) =1 per two minute

b) poisson distribution is appropriate

P(x; μ) = (e^-μ) (μ^x) / x!

c) the expected number of occurence in one hour is the mean of two minutes multiplied by the number of period of 2 minutes

= 1*30=30

d)

the expected number of occurence in five minute is the mean of two minutes multiplied by the number of period of 2 minutes

= 1*2.5 = 2.5

evaluate the formula for x=3 and = 2.5

P(x; μ) = (e^-μ) (μ^x) / x!

P(3; 2.5) = (e^-2.5) (2.5³) / 3!

0.2138

e)

the expected number of occurence in ten minute is the mean of two minutes multiplied by the number of period of 2 minutes

= 1*5 = 5

evaluate the formula for x=0 and = 5

P(x; μ) = (e^-μ) (μ^x) / x!

P(0; 5) = (e-5) (5⁰) / 0!

0.0067

f)

the expected number of occurence in ten minute is the mean of two minutes multiplied by the number of period of 2 minutes

= 1*5 = 5

evaluate the formula for x=5 and = 5

P(x; μ) = (e^-μ) (μ^x) / x!

P(0; 5) = 1-(e-5) (5⁵) / 5!

0.8255

g)

the expected number of occurence in 15 minute is the mean of two minutes multiplied by the number of period of 2 minutes

= 1*7.5 = 7.5

evaluate the formula for x=7 and = 7.5

P(x; μ) = (e^-μ) (μ^x) / x!

P(0; 5) = (e^-7.5) (7.5⁷) / 7!

0.1456