Question

If Y is distributed N(5,100), find Pr (Y ≤ 8)

If Y is distributed N(2,25), find Pr(Y > 4)

If Y is distributed N(2,16), find Pr(4 ≤ Y ≤ 9)

Answer 1

1) If Y is distributed N(5,100), find Pr (Y ≤ 8)

where 5 is the population mean, 100 population variance

standard deviation = sqrt(100) = 10

standard normal variate Z =

Given Y = 8, = 5, = 10

Z = (8 - 5)/10 = 0.3

P(Y≤ 8) = P(Z≤ 8) = 0.6179

2) If Y is distributed N(2,25), find Pr(Y > 4)

given Y = 4

Z = (4 - 2)/5 = 0.4

Pr(Y > 4) = P(Z>0.4) = 1 - P(Z<=0.4) = 1 - 0.6554 =0.3446

3)

If Y is distributed N(2,16), find Pr(4 ≤ Y ≤ 9)

for Y = 4, Z = (4 - 2) / 4 = 0.5

for Y = 9, Z = (9 - 2) / 4 = 1.75

Pr(4 ≤ Y ≤ 9) = P(Z<1.75) - P(Z<0.5) = 0.2685