Question

The random variable Z follows a normal distribution with a mean of 0 and a standard deviation of 1.

1.

What is P(Z ≤ -1.54)? Include 4 decimal places in your answer.

2.

What is P(Z ≥ 0.45)? Include 4 decimal places in your answer.

3.

What is P(-1.25 ≤ Z ≤ 0.65)? Include 4 decimal places in your answer.

4.

What is the 45^th percentile of Z? That is, what is the value of Z where the cumulative probability is 0.45? Include 2 decimal places in your answer.

Answer 1

SOLUTION:

1.

P(Z ≤ -1.54)=0.0618

2.

P(Z ≥ 0.45) = 1- P(Z ≤ 0.45)

=1-0.6736

=0.3264

3.

P( -1.25 z 0.65)

= P(z 0.65) - P(z -1.25)

=0.7422-0.1056

=0.6366

4.

P(Z < z) = 45%

= P(Z < z) = 0.45

= P(Z < -0.13) = 0.45

z =-0.13 Using standard normal z table,