Answer to Question #147977 in Statistics and Probability for Vladimyr Lubin

Question

(Exa) 1. Find what is the probability of value of X being equals <=110 for the normal distribution defined by the average of 92 and standard deviation of 14. Score?

2. What would be the probability of X being >110 mean is 92 and the standard deviation is 14 (Remember total probability is 1!) Score?

Answer 1

1)

$$P(X\leq110)=P(Z\leq\dfrac{110-92}{14})=P(Z\leq\dfrac{9}{7})$$

$$\approx P(Z\leq1.285714)\approx0.90072860$$

2)

$$P(X>110)=1-P(X\leq110)$$

$$=1-P(Z\leq\dfrac{110-92}{14})=1-P(Z\leq\dfrac{9}{7})$$

$$\approx 1-P(Z\leq1.285714)\approx1-0.90072860$$

$$\approx0.09927140$$