for a standard normal distribution, find the approximate value of p(z≥ - 1.25). use the portion of the…

for a standard normal distribution, find the approximate value of p(z≥ - 1.25). use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.25 0.5987 1.00 0.8413 1.25 0.8944 1.50 0.9332 1.75 0.9599 11% 39% 61% 89%
Answer
Answer:
89%
Explanation:
Step1: Recall normal - distribution property
The total area under the standard - normal curve is 1.
Step2: Find $P(Z < 1.25)$
From the table, $P(Z < 1.25)=0.8944$.
Step3: Use the complement rule
$P(Z\geq1.25)=1 - P(Z < 1.25)$.
Step4: Calculate the result
$P(Z\geq1.25)=1 - 0.8944 = 0.1056\approx0.11$ (for $P(Z\geq1.25)$). But we want $P(Z\geq - 1.25)$. Since the standard - normal distribution is symmetric about $z = 0$, $P(Z\geq - 1.25)=P(Z < 1.25)+P(Z\geq1.25)$ and also $P(Z\geq - 1.25)=1 - P(Z < - 1.25)$. And because of symmetry $P(Z < - 1.25)=1 - P(Z < 1.25)$. So $P(Z\geq - 1.25)=P(Z < 1.25)=0.8944\approx89%$.