Question

Q1. Suppose that Z has a standard normal distribution (with mean 0 and a standard deviation of 1, as in Table E.2). a. What is the probability that:

i) Z is less than 1.45

ii) Z is greater than 1.55

iii) Z is between 1.45 and 1.55

b. What is the value of Z if only 10% of all possible Z values are larger?

Answer 1

Z is the standard normal variable with

mean=0

Standard deviation = 1

1. Probability of getting z < 1.45

By the z-table we get z(1.45) = 0.0735

Probability of getting z<1.45 is = 1-0.0735 = 0.9265

2 Probabality of getting Z > 1.55

Using z-table z(1.55) = 0.0606

So the probabality of getting Z>1.55 = 0.0606

3. Between 1.45 and 1.55

Probability of getting value between 1.45 and 1.55

= 0.0735-0.0606

= 0.0129

b. We search the value 0.10 in z value

We get 1.28 = 0.1003

So the z value for only hai 10% are larger and 90% is smaller is z= 1.28

We can also use this formula for getting the z values