For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3340. What is the value of Z?
A) 0.37
B) 0.97
C) 1.06
D) 0.07

Question

Quizplus · Accepted Answer

Using a normal distribution table or calculator, we can find the Z-score that corresponds to a probability of 0.3340 being between 0 and Z. This Z-score is approximately 0.409. Therefore, we can set up the equation:

P(0 < Z < 0.409) = 0.3340

Using a normal distribution table or calculator again, we can find that the probability of a standard normal variable being between 0 and 0.409 is 0.1629. So we can set up another equation:

P(Z < 0.409) - P(Z < 0) = 0.1629

Solving for the Z-score, we get:

Z = 0.97

Therefore, the value of Z that corresponds to a probability of 0.3340 being between 0 and Z is approximately 0.97. The answer is B.

For Some Positive Value of Z, the Probability That a Standard