Question

Compute the following probabilities:

a. If Y is distributed N (-8,9), Pr (Y≤-12) = —— . (Round your response to four decimal places.)
b. If Y is distributed N (-4,9), Pr (Y>-1) = ——. (Round your response to four decimal places.)
c. If Y is distributed N (40,25), Pr (34≤Y≤44) = ——. (Round your response to four decimal places.)

Answer 1

Answer: a. 0.3300 b. 0.3707 c. 0.1584

Step-by-step explanation:

If X is distributed N(
`\mu,\sigma^2`) [Normal distribution], then Z-score =
`(X-\mu)/(\sigma)` .

a. If Y is distributed N (-8,9),

Pr (Y≤-12)
`=P((Y-\mu)/(\sigma)\leq (-12-(-8))/(√(9)))`

`=P(Z\leq -1.33)=1-P(Z<1.33)\\\\=1- 0.9082\ \ \ [\text{By z-table}]\\\\= 0.0917`

b. If Y is distributed N (-4,9),

Pr (Y>-1) =
`=P((Y-\mu)/(\sigma)>(-1-(-4))/(3))`

`=P(Z>1)=1-P(Z<1)\\\\=1-0.8413\ \ \ [\text{By z-table}]\\\\=0.1587`

c. If Y is distributed N (40,25),

Pr (34≤Y≤44) =
`P((34-40)/(5)<(Y-\mu)/(\sigma)<(44-40)/(5))`

`P(-1.2<Z<0.8)=P(Z<0.8)-P(Z<-1.2)\\\\=P(Z<0.8)-(1-P(Z<1.2))\\\\=0.7881-(1-0.8849)\ \ \ [\text{By z-table}]\\\\=0.6730`