STA 2023 Quiz 4 Solutions.pdf - Name Panther ID Spring 2018...

Name: _________________________
Panther ID: _________________________
Spring 2018
STA 2023 – Statistics for Business & Economics
Quiz # 4 Solutions
There are 2 problems for a total of 20 points. Show your work. Please write your work neatly.
Problem 1 (10 points). Let Y be a normal random variable having μ = -5 and σ 2 =9.
a) Compute P(-7 < Y < -2)
𝑃(−7 < ? < −2) = 𝑃(? < −2) − 𝑃(? < −7)
= 𝑃 (? <
−2 − (−5)
3
) − 𝑃 (? <
−7 − (−5)
3
)
= 𝑃(? < 1) − 𝑃 (? < −
2
3
)
= 0.8413 − [1 − 0.7486]
= 𝟎. ????.
b) Compute P(|Y+2 |≥ 2).
𝑃(|? + 2| ≥ 2) = 𝑃(? > 0) + 𝑃(? < −4)
= 𝑃 (? >
5
3
) + 𝑃 (? <
1
3
)
= [1 − 0.9525] + 0.6293
= 𝟎. ????
c) Find y
0
so that P(Y> y
0
)=0.85.
P (
? + 5
3
>
𝑦
0
+ 5
3
) = 0.85
P (? >
𝑦
0
+ 5
3
) = 0.85
Therefore,
−(𝑦
0
+5)
3
= 1.04 ; -y
0
= 3.12+5 and y
0
= -8.12 .

Problem 2 (10 points). Suppose that the population of FIU students have an average height of 67 inches