Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Probability Distributions

Question:

Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).

Assertion (A): The area under the standard normal curve which lies right of Z = -0.48 is F(0.48).
Reason (R): If Z is a standard normal variable, then F(z) represents the entire area which is left of the line Z = z.

Select the correct answer from the options given below.

Options:

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Assertion (A) is true, but Reason (R) is false.

Assertion (A) is false, but Reason (R) is true.

Correct Answer:

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Explanation:

The correct answer is Option (2) → Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Area under the standard normal curve to the right of $Z = -0.48$

$= P(Z > -0.48) = 1-P(Z<-0.48)$

$=1-F(-0.48) = 1-(1-F(0.48))$

$=1-1+F(0.48) = F(0.48)$.

∴ Assertion is true.

Also, Reason is true.

Reason is not the correct explanation of Assertion.