For a standard normal variable $Z$ , what is the probability that $- 1.5 l e Z l e 1.5$ ?

hard MCQ 4 marks Class 11 · Mathematics · Statistics

Answer

0.8664

The correct answer is 0.8664 — Subtract to obtain the probability between the two limits: $0.9332 - 0.0668 = 0.8664$ .

Step-by-step solution

From the standard normal table, find $P (Z l e 1.5) = 0.9332$ .
Find $P (Z l e - 1.5)$ . For a symmetric distribution, $P (Z l e - 1.5) = 1 - P (Z l e 1.5) = 1 - 0.9332 = 0.0668$ .
Subtract to obtain the probability between the two limits: $0.9332 - 0.0668 = 0.8664$ .

Common mistake: Subtracting the larger probability from the smaller instead of vice versa

Concept tested: Probability between two z‑scores in normal distribution