Question

Y ∼ N (10, 36), What are probabilities of...

1. Y > 10

2. Y > 11

3. |Y − 11| > 1

4. Y/2 > 5

5. Y/2 > 4

6. |(Y/2) − 4| > 1

Answer 1

We would be looking at the first 4 parts here as:

We are given the distribution here as:

a) The probability here is computed as:

P(Y > 10)

As 10 is the mean and normal distribution is symmetric about its mean, therefore:
P(Y > 10) = P(Y < 10) = 0.5

Therefore 0.5 is the required probability here.

b) The probability here is computed as:

P(Y > 11)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.4338 is the required probability here.

c) The probability here is computed as:

This can be also written as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.8694 is the required prob. here.

d) P(Y / 2 > 5)

= P(Y > 10)

Already computed in the first part as 0.5

Therefore 0.5 is the required prob. here.