Question

4) A typical typist's accuracy is 1450 words in 15000 words. What is the probability that this typist makes 4 errors in 550 words? 5) A specific drive through receives 3 customers every 30 minutes on average. (a) What is the expected value of customers for them in an hour? (b) What is the probability that they receive exactly 5 customers in the next 90 minutes? (c) What is the chance that they do not receive any customers in the next 60 minutes? (d) What is the probability that they receives exactly 5 customers in the next 30 minutes?

Answer 1

Answer:

4.

Given,

x = 1450

sample n = 15000

sample proportion p^ = x/n = 1450/15000 = 0.097

P(X = 4) = 550C4*0.097^4*(1-0.097)^(550-4)

= 0 [less than 0.000001]

= 0

5.

Given,

Rate of customers = 3/30 = 0.1 /min

a)

Expected value = rate*60 min

= 0.1*60

= 6

b)

lamda = 0.2*90 = 18

P(X = 5) = e^-18*18^5/5!

= 0.00024

c)

lamda = 0.2*60 = 12

P(X = 0) = e^-12*12^0/0! = 0.0000006

d)

lamda = 0.2*30 = 6

P(X = 5) = e^-6*6^5/5!

= 0.16062