Independent solution

How to solve this Normal Distribution question

Setup

Setup

Write the first company's loss threshold in standard-normal units using the positive common mean mu.

σA=μ2\sigma_A=\frac{\mu}{2}
Pr⁡(A<0)=Φ(−μσA)=Φ(−2)=0.0227501\Pr(A<0)=\Phi\left(-\frac{\mu}{\sigma_A}\right)=\Phi(-2)=0.0227501

Model

Model

Apply the stated probability factor, then identify the standardized distance for the second company.

Pr⁡(B<0)=0.9Φ(−2)=0.0204751\Pr(B<0)=0.9\Phi(-2)=0.0204751
Φ(−μσB)=0.0204751\Phi\left(-\frac{\mu}{\sigma_B}\right)=0.0204751

Compute

Compute

Invert the normal CDF and compare each standard deviation with the shared mean.

Φ−1(0.0204751)=−2.0440335\Phi^{-1}(0.0204751)=-2.0440335
σBσA=μ/2.0440335μ/2=22.0440335=0.9784575\frac{\sigma_B}{\sigma_A}=\frac{\mu/2.0440335}{\mu/2}=\frac{2}{2.0440335}=0.9784575

Answer

Answer

The standard deviation ratio rounds to 0.98.

0.98(C)\boxed{0.98\quad\text{(C)}}