Question

find the probability using the normal distribution: ( p(1.17 < z < 1.23) ). use the standard normal distribution table and enter the answer to 4 decimal places.

( p(1.17 < z < 1.23)=square )

Explanation:

Step1: Use the property of normal distribution

For a standard normal variable \(z\), \(P(a < z < b)=P(z < b)-P(z < a)\)
Here \(a = 1.17\) and \(b=1.23\)
So \(P(1.17 < z < 1.23)=P(z < 1.23)-P(z < 1.17)\)

Step2: Look up values in the standard - normal table

From the standard normal distribution table:
\(P(z < 1.23)\):
For \(z = 1.23\), we look at the row corresponding to \(1.2\) and the column corresponding to \(0.03\). The value is \(0.8907\)
\(P(z < 1.17)\):
For \(z = 1.17\), we look at the row corresponding to \(1.1\) and the column corresponding to \(0.07\). The value is \(0.8790\)

Step3: Calculate the probability

\(P(1.17 < z < 1.23)=0.8907 - 0.8790\)
\(P(1.17 < z < 1.23)=0.0117\)

Answer:

\(0.0117\)