Question

For Exercises find the area under the standard normal distribution curve.

Between z = 0 and z = 1.77

Answer 1

We are supposed to find the area under the standard normal distribution curve between z = 0 and z = 1.77. That is we are supposed to find P(0 ≤ z ≤ 1.77).

 

The area under the standard normal curve to the left of z = 1.77 is 0.9616 (from standard normal table). That is, P(z < 1.77) = 0.9616.

 

The area under the standard normal curve to the left of z = 0 is 0.5000 (from standard normal table). That is, P(z < 0) = 0.5000.

 

Therefore, the required probability is as obtained below.

P(0 < z < 1.77) = P(z ≤ 1.77) – P(z ≤ 0)

                          = 0.9616 – 0.5000

                         = 0.4616

 

Hence the probability is 0.4616 or 46.16%.

 

The area under the normal curve is given below.

 

Therefore, the area under the standard normal distribution curves between z = 0 and z = 1.77 is 0.4616.

Therefore, the area under the standard normal distribution curves between z = 0 and z = 1.77 is 0.4616.