Question

if Z is a standard normal variable, find the probability. p(-0.73< z<2.27)

Answer 1

We use the Z table to find the probabilities

$P(-0.73-0.73)$

We first calculate the largest value of z

$P(z<2.27)=0.9884$

In the table there are no negative values, it is not -0.73. But the graph is symmetric about the mean, about 0. Then

$\begin{gathered} P(z<-0.73)=P(z<0.73) \\ P(z<0.73)=0.7673 \end{gathered}$

Since the value we want is z>-0.73

$P(z>-0.73)=1-P(z<-0.73)$$\begin{gathered} P(z>-0.73)=1-0.7673 \\ P(z>-0.73)=0.2327 \end{gathered}$

Now we calculate the value of the probability that we want by substituting the values

[tex]\begin{gathered} P(-0.73-0.73) \\ P(-0.73The probability is 75.57%[tex]P(-0.73