for a standard normal distribution, find the approximate value of p(-0.78≤z≤1.16). use the portion of the…

for a standard normal distribution, find the approximate value of p(-0.78≤z≤1.16). use the portion of the standard normal table below to help answer the question.\n| z | probability |\n| ---- | ---- |\n| 0.00 | 0.5000 |\n| 0.16 | 0.5636 |\n| 0.22 | 0.5871 |\n| 0.78 | 0.7823 |\n| 1.00 | 0.8413 |\n| 1.16 | 0.8770 |\n| 1.78 | 0.9625 |\n| 2.00 | 0.9772 |\n22%\n66%\n78%\n88%

for a standard normal distribution, find the approximate value of p(-0.78≤z≤1.16). use the portion of the standard normal table below to help answer the question.\n| z | probability |\n| ---- | ---- |\n| 0.00 | 0.5000 |\n| 0.16 | 0.5636 |\n| 0.22 | 0.5871 |\n| 0.78 | 0.7823 |\n| 1.00 | 0.8413 |\n| 1.16 | 0.8770 |\n| 1.78 | 0.9625 |\n| 2.00 | 0.9772 |\n22%\n66%\n78%\n88%

Answer

Explanation:

Step1: Recall property of standard - normal distribution

$P(-0.78\leq z\leq1.16)=P(z\leq1.16)-P(z\leq - 0.78)$. Since the standard - normal distribution is symmetric about $z = 0$, $P(z\leq - 0.78)=1 - P(z\leq0.78)$.

Step2: Look up values in the table

From the table, $P(z\leq1.16) = 0.8770$ and $P(z\leq0.78)=0.7823$. Then $P(z\leq - 0.78)=1 - 0.7823=0.2177$.

Step3: Calculate the probability

$P(-0.78\leq z\leq1.16)=P(z\leq1.16)-P(z\leq - 0.78)=0.8770-0.2177 = 0.6593\approx0.66$.

Answer:

$66%$