Another probability question?

Question

A distribution of IQ scores have a mean of 100 and standard deviation of 15. (Normal distribution)

A. What's the probability a student has IQ of 90 or less?
B. IQ of 120 or less?
C. IQ between 120 and 90?
D. IQ greater than 130?

Please show examples.

Answer 1

IQ between 120 and 90?

z1=(120-100)/15=20/15=4/3=1.33
z2=(90-100)/15=-10/15=-2/3=-0.66
P(90 0.245373+0.408241

Answer 2

Z = (X - µ)/σ , where Z is found in the standard normal table and with it is associated the cumulative probability. The notation I'll use is Φ[Z] gives the probability.
A. Z = (90 - 100)/15 = -10/15 = - 0.67; Φ[-0.67] = 0.2514
B. Below 120: Z = (120 - 100)/15 = 1.33; Φ[1.33] = 0.9082
Below 90: 0.2514 (from A); so probability between 120 and 90 is 0.9082 - 0.2514 = 0.657
C. Z= (130 - 100)/15 = 2.0; Φ[2.0] = 0.9772; so the probability greater than is 1 - 0.9772 = 0.0228

Answer 3

a. 25.25%

b. 90.88%

c. 90.88 - 25.25 = 65.63%

d. 100 - 97.72 = 2.28%