Solve the problem.
-Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $\mathrm { P } ( 0

Question

Solve the problem.
-Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $\mathrm { P } ( 0 < \mathrm { z } < \mathrm { a } ) = 0.4608$ find a.
A) 1.76
B) -0.10
C) 0.61
D) 0.1772

Quizplus · Accepted Answer

Since the mean is 0 and the standard deviation is 1, we know that the area to the left of z = 0 is 0.5 (since it's a standard normal distribution). We also know that the area between z = 0 and z = a is 0.4608. To find the area to the right of z = a, we can subtract the area between z = 0 and z = a from the total area to the right of z = 0:

Area to the right of z = a = 0.5 - 0.4608 = 0.0392

Using a standard normal distribution table or calculator, we can find the z-score corresponding to an area of 0.0392 to be approximately 1.76. Therefore, the answer is choice A: 1.76.

Solve the Problem P(0<z<a)=0.4608\mathrm { P } ( 0 < \mathrm { z } < \mathrm { a } ) = 0.4608P(0<z<a)=0.4608

Solve the Problem $\mathrm { P } ( 0 < \mathrm { z } < \mathrm { a } ) = 0.4608$