Question

1. Using the following uniform density curve, determine what is the probability that a random variable has a value less than 44?

-2 6 8 " 10 12

SELECT ALL APPLICABLE CHOICES

A)

44.444%44.444%

B)

56.222%56.222%

C)

53.889%53.889%

D)

30.556%30.556%

E)

75.556%75.556%

F)

63.556%63.556%

G)

55.556%55.556%

None of These

2.

Using the following uniform density curve, determine what is the probability that a random variable has a value between 33 and 1212 ?

SELECT ALL APPLICABLE CHOICES

A)

50.909%50.909%

B)

44.909%44.909%

C)

40.909%40.909%

D)

30.909%30.909%

E)

42.242%42.242%

F)

39.909%39.909%

G) None of These

Answer 1

ANSWERS:

1)

A) 44.444%

2)

C) 40.909%

EXPLANATION:

1.)

Here, we have uniform distirbution with b = 9 and a = 0.

The CDF is given by

F(x) = 0, for x < 0

$F(x) =\frac{x-a}{b-a}$

F(x) = (x -0)/(9-0) = x/9 for 0 < x < 9

F(x) = 1 for x > 22

For, x<4,

P(X<4) = 4/9 = 0.4444

= 44.44%

2)

1.)

Here, we have uniform distirbution with b = 22 and a = 0.

The CDF is given by

F(x) = 0, for x < 0

$F(x) =\frac{x-a}{b-a}$

F(x) = (x -0)/(22-0) = x/22 for 0 < x < 22

F(x) = 1 for x > 22

For, 3 < x <12,

P( 3 < x <12,) = P(X<12) -P(X<3)

=12/22 - 3/22

=9/22

=0.40909

= 40.909%