Question

find the area of the shaded region under the standard normal distribution between the given z - scores.
round your answer to four decimal places.

question help: \\( \square \\) message instructor
\\( p(-2.33<z<-1.68)= \\)

Explanation:

Step1: Use the property of normal distribution

We know that for a standard normal distribution \(Z\), \(P(a < Z < b)=P(Z < b)-P(Z < a)\). Here \(a=-2.33\) and \(b = - 1.68\).

Step2: Look up the values in the standard - normal table

From the standard - normal table (z - table), \(P(Z < - 1.68)=0.0465\) and \(P(Z < - 2.33)=0.0099\).

Step3: Calculate the probability

\(P(-2.33 < Z < -1.68)=P(Z < - 1.68)-P(Z < - 2.33)\)
Substitute the values: \(P(-2.33 < Z < -1.68)=0.0465 - 0.0099\)
\(P(-2.33 < Z < -1.68)=0.0366\)

Answer:

\(0.0366\)