which is equivalent to p(z ≥ 1.4)?\np(z ≤ 1.4)\n1 - p(z ≤ 1.4)\np(z ≥ -1.4)
which is equivalent to p(z ≥ 1.4)?\np(z ≤ 1.4)\n1 - p(z ≤ 1.4)\np(z ≥ -1.4)
Answer
Answer:
B. $1 - P(z\leq1.4)$
Explanation:
Step1: Recall total - probability rule
The total area under the standard normal curve is 1. That is, $P(-\infty<z<\infty) = 1$.
Step2: Split the probability
We know that $P(-\infty<z<\infty)=P(z < 1.4)+P(z\geq1.4)$.
Step3: Solve for $P(z\geq1.4)$
Rearranging the equation $P(-\infty<z<\infty)=P(z < 1.4)+P(z\geq1.4)$ gives $P(z\geq1.4)=1 - P(z < 1.4)$. Since $P(z < 1.4)=P(z\leq1.4)$ (because the probability at a single point in a continuous distribution is 0), we have $P(z\geq1.4)=1 - P(z\leq1.4)$.