Hello, I really need help explaining how these problems are figured out. I have the correct answers listed, because this was my homework assignment that was corrected. I just need to learn how they are coming up with some of these numbers.

Thank you!

Stanford-Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 16.

(b)Write the equation that gives the z score corresponding to a Stanford-Binet IQ test score.

z=(x -100)/16 I understand this!

(c)Find the probability that a randomly selected person has an IQ test score. (Round answers to 4 decimal places.)

1.P(x > 140) = P(z>2.5) I understandhow they got2.5 because 140-100/16 =2.5 butwhere does the0.9938 come from?to get the answer for the problem 1-.9938 =0.0062

2.P(x < 88)= p(z<-.75) = 0.2266Can you please describe how they comeup with this answer

3.P(72 < x < 128)= P(-1.75I really have no idea how they get any of these numbers.. especially .9599 and .0401

4.P(-1.5 < z < 1.5) = .9332-.0668 = .8664 I have no idea how this is figured out either please explain in detail

(d)Suppose you take the Stanford-Binet IQ Test and receive a score of 136. What percentage of people would receive a score higher than yours? (Answer as a percentage, rounded to two decimal places, without the percentage (%)symbol.)

p(x>136)=P(z>2.25)=1 -.9878 = 1.22% How do they come up with .9878 to subtract from 1 for the answer?