Question

Compute the following probabilities:
a. If Y is distributed N(3, 3), find Pr(Y ≤ 3).
b. Y is distributed N(-1, 25), find Pr(Y > 0).
c. Y is distributed N(5, 25), find Pr(0 ≤ Y ≤ 10)

Answer 1

Solution :

Given that ,

a) Y is distributed N(3, 3), find Pr(Y ≤ 3).

mean = = 3

variance = ² = 3

standard deviation = = ² = 3 = 1.73

P(Y 3)

= P[(Y - ) / (3 - 3) / 1.73 ]

= P(z 0)

Using z table,

=0.5

b) Y is distributed N(-1, 25)

mean = = -1

variance = ² = 25

standard deviation = = ² = 25 = 5

P(Y > 0) = 1 - p( Y < 0)

=1- p P[(Y - ) / < (0 - (-1)) / 5]

=1- P(z < 0.2)

Using z table,

= 1 - 0.5793

= 0.4207

c) Y is distributed N(5, 25),

mean = = 5

variance = ² = 25

standard deviation = = ² = 25 = 5

P(0 Y 10)

= P[(0 - 5 / 5) (Y - ) / (10 - 5 / 5) ]

= P(-1.0 z 1.0)

= P(z 1.0) - P(z -1.0)

Using z table,  

= 0.8413 - 0.1587

= 0.6826