Normal Distribution and Answer

Question 1
The following table gives the classification of the amount paid and the method of payment at a department store.

Cash
Credit
Debit
Total
< $20
10
8
6
24
$20 - $100
15
25
10
50
Over $100
5
15
6
26
Total
30
48
22
100

a) Find the probability that the amount paid is < $20 Answer: P(<$20) = b) Find the probability that the method of payment is credit Answer: P(Credit) = c) Find the probability that the amount is <$20 and the method of payment is credit? Answer: P(<$20) = d) Find the probability that the amount is <$20 or the method of payment is credit

Answer: P(<$20 OR credit) =

e) Given that the method of payment is credit, what is the probability that the amount is <$20

Answer: P(<$20/credit) =

(Question 2) John and Jane are married. The probability that John watches a certain television show is .4. The probability that Jane watches the show is .5. The probability that John watches the show, given that Jane does, is .7.

a) Find the probability that both John and Jane watch the show. Answer: A : John watches a certain television show B: Jane watches the show P(A) = 0.4 P(B) = 0.5 P( A/B) = 0.7 P(A/B) = 0.7 = P(A and B)

b) Find the probability that Jane watches the show, given that John does. Answer: P(B/A) = P(B/A)= P(A and B)

c) Do John and Jane watch the show independently of each other? Justify your answer.

Answer: The two event are not independent because: P(A and B) P(A). P(B) = 0.4 x 0.5 = 0.20 P(A and B) P(A). P(B) So the two event no (independent)

Question 3
Consider the following probability mass function x -2
0
1
2
P(X= x)
.2
.3
.3
.2

Find the following:
a) P (X < 1) Answer: P