which of the following probabilities is equal to approximately 0.2957? use the portion of the standard…

which of the following probabilities is equal to approximately 0.2957? use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.25 0.5987 0.50 0.6915 0.75 0.7734 1.00 0.8413 1.25 0.8944 1.50 0.9332 1.75 0.9599 p(-1.25≤z≤0.25) p(-1.25≤z≤0.75) p(0.25≤z≤1.25) mark this and return save and exit next submit

which of the following probabilities is equal to approximately 0.2957? use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.25 0.5987 0.50 0.6915 0.75 0.7734 1.00 0.8413 1.25 0.8944 1.50 0.9332 1.75 0.9599 p(-1.25≤z≤0.25) p(-1.25≤z≤0.75) p(0.25≤z≤1.25) mark this and return save and exit next submit

Answer

Explanation:

Step1: Recall the property of standard - normal table

The standard - normal table gives $P(Z\leq z)$. For $P(a\leq Z\leq b)=P(Z\leq b)-P(Z\leq a)$.

Step2: Calculate $P(- 1.25\leq Z\leq0.25)$

$P(-1.25\leq Z\leq0.25)=P(Z\leq0.25)-P(Z\leq - 1.25)$. Since the standard - normal distribution is symmetric about $z = 0$, $P(Z\leq - 1.25)=1 - P(Z\leq1.25)$. So $P(-1.25\leq Z\leq0.25)=P(Z\leq0.25)-(1 - P(Z\leq1.25))$. From the table, $P(Z\leq0.25)=0.5987$ and $P(Z\leq1.25)=0.8944$. Then $P(-1.25\leq Z\leq0.25)=0.5987-(1 - 0.8944)=0.5987 - 0.1056=0.4931$.

Step3: Calculate $P(-1.25\leq Z\leq0.75)$

$P(-1.25\leq Z\leq0.75)=P(Z\leq0.75)-P(Z\leq - 1.25)=P(Z\leq0.75)-(1 - P(Z\leq1.25))$. From the table, $P(Z\leq0.75)=0.7734$ and $P(Z\leq1.25)=0.8944$. Then $P(-1.25\leq Z\leq0.75)=0.7734-(1 - 0.8944)=0.7734 - 0.1056 = 0.6678$.

Step4: Calculate $P(0.25\leq Z\leq1.25)$

$P(0.25\leq Z\leq1.25)=P(Z\leq1.25)-P(Z\leq0.25)$. From the table, $P(Z\leq1.25)=0.8944$ and $P(Z\leq0.25)=0.5987$. Then $P(0.25\leq Z\leq1.25)=0.8944 - 0.5987=0.2957$.

Answer:

$P(0.25\leq z\leq1.25)$