Question

Find each of the following probabilities for a normaldistribution.a. p(z > 2.25)b. p(z > −1.20)c. p(z < 0.40)d. p(z < -1.75)

Answer 1

We need to find the probabilities for each required z-score.

A z-score table shows the probability associated with values less than a specific z-score.

Thus, in order to use a z-score table to solve this problem, we need to notice that the probability that z is greater than a certain number equals the whole probability (1) minus the probability that z is less than that number.

The probability associated with a z-score less than 2.25 is shown above.

We have the table below with some negative z-scores:

Thus, we have:

`\text{ a. }p\left(z>2.25\right)=1-p(z<2.25)\cong1-0.9878=0.0122`
`\text{ b. }p\left(z>−1.20\right)=1-p(z<-1.20)\cong1-0.1151=0.8849`
`\text{ c. }p\left(z<0.40\right)=0.6554`
`\text{ d. }p\left(z<-1.75\right)=0.0401`

Answers

a. 0.0122

b. 0.8849

c. 0.6554

d. 0.0401