Question

1) Suppose that X ∼ N(0,1) find:

P(X<=1.36)
Round your answer to the nearest thousandth.

2) Suppose that X ∼ N(0,1) find:

P(|X-0.9|>=1.35)

Round your answer to the nearest thousandth.

3)Suppose that X ∼ B(8, 0.25).

Calculate p(X=1)

Round your answer to the nearest thousandth.

4) Suppose that X ∼ B(10, 0.23).

Calculate P(X ≥ 7)

Round your answer to the nearest thousandth.

5)Suppose that X ∼ U(-5, 10).

Find the P(-2 ≤ X ≤ 5)

Round your answer to the nearest thousandth.

6) Suppose that X ∼ N(-1.5,2.6), Y ∼ N(2.7,1.4), and Z ∼ N(1.4, 0.9) are independent random variables.

Find the probability that |2.4X + 3Y + 4Z| ≥ 10.7.

Round your answer to the nearest thousandth.

Answer 1

1)

Here X has standard normal distribution. Using z-table we have

Answer: 0.913

2)

Now,

P (1X-0.9| > 1.35)-P(X_ 0.9 <ー1.35)+P(X-0.9 > 1.35) P(X 0.9 1.35) PX 0.9+1.35)

Answer: 0.339

3)

Answer: 0.267

4)

Answer: 0.002