Answer to Question #277097 in Statistics and Probability for WAFA

Question

If the random variable x follows a normal distribution with a mean of 18 and a standard deviation of 5, find the value of k such that

1-p(X>K)=0.2578

2-p(X<K)=0.2578

Answer 1

$\mu=18 \\ \sigma = 5$

1.

$P(X>K) = 0.2578 \\ 1 -P(X<K) =0.2578 \\ P(X<K) = 0.7422 \\ P(Z< \frac{K-18}{5}) = 0.7422 \\ \frac{K-18}{5} = 0.6505 \\ K -18 = 5 \times 0.6505 \\ K = 18 +3.2525 = 21.2525$

2.

$P(X<K)=0.2578 \\ P(Z< \frac{K-18}{5}) = 0.2578 \\ \frac{K-18}{5} = -0.65 \\ K-18 = 5 \times (-0.65) \\ K = 18 -3.25 = 14.75$