Question

X is normally distributed with a mean of 0.60 and a standard deviation of 0.53.

a. Find the value of x that solves P(X ≤ x)= 0.55

b. Find the value of x that solves P(X > x)= 0.75

c. Find the value of x that solves P(x <X ≤ 0.76) = 0.35

d. Find the value of x that solves P(0.49 < X ≤x) = 0.30

Answer 1

Let ,

a.

...........(1)

Also , from standard normal probability table ,

...........(2)

From (1) and (2) we get ,

Therefore , the value of x is 0.6689

b.

...........(1)

Also , from standard normal probability table ,

...........(2)

From (1) and (2) we get ,

Therefore , the value of x is 0.2449

c.

.............(1)

Also , from standard normal probability table ,

................(2)

From (1) and (2) , we get ,

Therefore , the value of the x is 0.2714

d.

.............(1)

Also , from standard normal probability table ,

................(2)

From (1) and (2) , we get ,

Therefore , the value of the x is 0.9021