Area between -1.96 to +1.96 in a normal distribution is:

Option b: 95%. Solution: Area Under Normal Curve for Standard Normal Limits For a standard normal variable Z N(0, 1) : Step 1: Identify standard critical values and confidence intervals From standard normal distribution tables, the probability that Z lies within certain standard standard deviation limits is: 1. P(-1 ≤ Z ≤ 1) ≈ 0.6827 = 68.27% 2. P(-2 ≤ Z ≤ 2) ≈ 0.9545 = 95.45% 3. P(-3 ≤ Z ≤ 3) ≈ 0.9973 = 99.73% Step 2: Determine area for z = ± 1.96 The value z = 1.96 is the critical value for a 95% confidence interval: P(-1.96 ≤ Z ≤ 1.96) ≈ 0.9500 = 95% Therefore, the area under the standard normal curve between z = -1.96 and z = 1.96 is exactly 95% , which corresponds to Option B. Hence, Option B is the correct answer.

Area between $-1.96$ to $+1.96$ in a normal distribution is:

The correct answer is Option b: $95\%$. **Area Under Normal Curve for Standard Normal Limits** For a standard normal variable $Z \\sim N(0, 1)$: **Step 1: Identify standard critical values and confidence intervals** From standard normal distribution tables, the probability that $Z$ lies within certain standard standard deviation limits is: 1. $P(-1 \\le Z \\le 1) \\approx 0.6827 = 68.27\%$ 2. $P(-2 \\le Z \\le 2) \\approx 0.9545 = 95.45\%$ 3. $P(-3 \\le Z \\le 3) \\approx 0.9973 = 99.73\%$ **Step 2: Determine area for $z = \\pm 1.96$** The value $z = 1.96$ is the critical value for a $95\%$ confidence interval: $$P(-1.96 \\le Z \\le 1.96) \\approx 0.9500 = 95\%$$ Therefore, the area under the standard normal curve between $z = -1.96$ and $z = 1.96$ is exactly $95\%$, which corresponds to Option B. Hence, **Option B** is the correct answer.

Theoretical DistributionsMCQMTP Dec 2022 Series IIQuestion 3541 of 230

All Questions

Area between $\displaystyle -1.96$ to $\displaystyle +1.96$ in a normal distribution is:

Options

\displaystyle 95.45\%

\displaystyle 95\%

\displaystyle 96\%

\displaystyle 99\%

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Correct Answer

✅ Option b — $\displaystyle 95\%$

All Options:

A $\displaystyle 95.45\%$
B $\displaystyle 95\%$
C $\displaystyle 96\%$
D $\displaystyle 99\%$

Detailed Solution & Explanation

**Area Under Normal Curve for Standard Normal Limits** For a standard normal variable

\displaystyle Z \\sim N(0, 1)

: **Step 1: Identify standard critical values and confidence intervals** From standard normal distribution tables, the probability that

\displaystyle Z

lies within certain standard standard deviation limits is: 1.

\displaystyle P(-1 \\le Z \\le 1) \\approx 0.6827 = 68.27\%

\displaystyle P(-2 \\le Z \\le 2) \\approx 0.9545 = 95.45\%

\displaystyle P(-3 \\le Z \\le 3) \\approx 0.9973 = 99.73\%

**Step 2: Determine area for

\displaystyle z = \\pm 1.96

** The value

\displaystyle z = 1.96

is the critical value for a

\displaystyle 95\%

confidence interval:

P(-1.96 \\le Z \\le 1.96) \\approx 0.9500 = 95\%

Therefore, the area under the standard normal curve between

\displaystyle z = -1.96

and

\displaystyle z = 1.96

is exactly

\displaystyle 95\%

, which corresponds to Option B. Hence, **Option B** is the correct answer.

About This Chapter: Theoretical Distributions

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Binomial, Poisson, Normal Distribution

This chapter covers Binomial, Poisson, Normal Distribution and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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Area between −1.96\displaystyle -1.96−1.96 to +1.96\displaystyle +1.96+1.96 in a normal distribution is: