Question

assume that the random variable x is normally distributed, with mean μ = 100 and standard deviation σ = 20. compute the probability p(x > 116).
0.2420
0.2119
0.7881
0.1977

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$. Here, $x = 116$, $\mu=100$, and $\sigma = 20$. So, $z=\frac{116 - 100}{20}=\frac{16}{20}=0.8$.

Step2: Find the probability using the standard normal distribution

We want $P(X>116)$, which is equivalent to $P(Z > 0.8)$ in the standard - normal distribution. Since the total area under the standard - normal curve is 1, and $P(Z>z)=1 - P(Z\leq z)$. Looking up $P(Z\leq0.8)$ in the standard - normal table, we find that $P(Z\leq0.8)=0.7881$. Then $P(Z > 0.8)=1 - 0.7881=0.2119$.

Answer:

0.2119