Question

3. Given μ_X = 8.3, σ_X = 3.2

a) Find prob(X < 10.0)

b) Find prob(X > 3.2)

c) Find X₀ such that prob(X > X₀) = .9573

d) Find prob(6.0 < X < 7.0)

e) Find the two X's that are the boundaries of the middle 68% of the distribution

Answer 1

a)

; From standard normal distribution table

b)

; From standard normal distribution table

c) Now ,

....................(I)

From standard normal distribution table , ...............(II)

From (I) and (II) , we get ,

d)

; From standard normal distribution table

e)

..............(I)

From standard normal distribution table , ...............(II)

From (I) and (II) , we get ,

And

Therefore , the x=11.47 and x=5.13