Independent solution

How to solve this Normal Distribution question

Answer in brief

The two upper-tail probabilities correspond to z-scores 0.449876 and 0.599859. Their 0.149984 difference spans 0.12 units, giving standard deviation 0.800088 and variance 0.640141, so choice B is correct.

Setup

Setup

Convert each upper-tail probability to its cumulative standard-normal z-score.

z1=Φ−1(1−0.3264)=0.4498757972…z_1=\Phi^{-1}(1-0.3264)=0.4498757972\ldots
z2=Φ−1(1−0.2743)=0.5998593133…z_2=\Phi^{-1}(1-0.2743)=0.5998593133\ldots

Model

Model

The difference between two standardized thresholds eliminates the unknown mean.

z2−z1=3.62−3.50σz_2-z_1=\frac{3.62-3.50}{\sigma}

Compute

Compute

Solve for the standard deviation and square it.

σ=0.120.5998593133−0.4498757972=0.8000879238…\sigma=\frac{0.12}{0.5998593133-0.4498757972}=0.8000879238\ldots
σ2=0.6401406858…\sigma^2=0.6401406858\ldots

Answer

Answer

The variance rounds to 0.64.

0.64(B)\boxed{0.64\quad\text{(B)}}