Problem

5 For a normal distribution, $P(X \leq 23.8)=91.92 \%$ and $P(X \leq 17.15)=30.85 \%$. Find the mean and standard deviation.

Answer

Expert–verified
Hide Steps
Answer

\boxed{\mu \approx 18.96, \sigma \approx 3.61}

Steps

Step 1 ：Given probabilities: $P(X \leq 23.8) = 91.92%$ and $P(X \leq 17.15) = 30.85%$

Step 2 ：Find corresponding z-scores: $z_1 = 1.34$ and $z_2 = -0.5$

Step 3 ：Set up system of equations using z-score formula: $1.34 = \frac{23.8 - \mu}{\sigma}$ and $-0.5 = \frac{17.15 - \mu}{\sigma}$

Step 4 ：Solve the system of equations for mean ($\mu$) and standard deviation ($\sigma$)

Step 5 ：\boxed{\mu \approx 18.96, \sigma \approx 3.61}

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More