Question

Assume that the random variable X is normally​ distributed, with mean mu equals 100 and standard deviation sigma equals 20. Compute the probability ​P(Xgreater than116​). 0.2119 0.7881 0.2420 0.1977

Answer 1

Answer: 0.2119

Step-by-step explanation:

We assume that the random variable X is normally​ distributed.

Given : Population mean : $\mu=100$

Standard deviation : $\sigma=20$

Z-score : $z=\dfrac{x-\mu}{\sigma}$

Then, z-score corresponds to 116

$z=\dfrac{116-100}{20}=0.8$

By using the standard normal distribution table for z , we have

$P(x>116)=P(z>0.8)=1-P(z\leq0.8)$

$=1-0.7881446\approx0.2119$

Hence, the required probability = 0.2119