Based on recent records, the manager of a car painting center has determined the

Question

Based on recent records, the manager of a car painting center has determined the following cumulative probabilities for X = the number of customers per day. (To hundredths)

What is the probability the center serves at most 3 customers in a day?

What is the probability the center serves less than 3 customers in a day?

What is the probability the center serves exactly 3 customers in a day?

What is the probability the center serves more than 3 customers in a day?

What is the probability the center serves no customers in a day?

Find the probability X is between 2 and 4 inclusive. That is, find P[2<=X<=4].

Find the probability X is between 3 and 6 inclusive. That is, find P[3<=X<=6].

P[ X <= x ] 0 0.05 1 0.25 2 0.55 3 0.80 4 0.95 5 1.00

Explanation / Answer

Ans:

1)P(atmost 3)=P(X<=3)=0.80

2)P(X<3)=P(X<=2)=0.55

3)P(X=3)=0.8-0.55=0.25

4)P(X>3)=1-P(X<=3)=1-0.8=0.20

5)P(x=0)=0.05

6)P(2<=X<=4)=0.3+0.25+0.15=0.70

7)P(3<=X<=6)=0.25+0.15+0.05=0.45

  

x P[ X <= x ] p(x) 0 0.05 0.05 1 0.25 0.2 2 0.55 0.3 3 0.8 0.25 4 0.95 0.15 5 1 0.05

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