Question

for a normal variable x ~ n(μ = 41.2, σ = 0.4), find the probability p(x > 40.9): p(x > 40.9) = (round the answer to 4 decimal places)

Explanation:

Step1: Standardize the value

We use the formula $Z=\frac{X - \mu}{\sigma}$. Here, $X = 40.9$, $\mu=41.2$, and $\sigma = 0.4$. So $Z=\frac{40.9 - 41.2}{0.4}=\frac{- 0.3}{0.4}=- 0.75$.

Step2: Find the probability using the standard - normal table

We want $P(X>40.9)$, which is equivalent to $P(Z>-0.75)$ in the standard - normal distribution. Since $P(Z > z)=1 - P(Z\leq z)$, and from the standard - normal table $P(Z\leq - 0.75)=0.2266$. Then $P(Z>-0.75)=1 - 0.2266 = 0.7734$.

Answer:

$0.7734$