Question

determine the area under the standard normal curve that lies to the right of (a) ( z = 0.82 ), (b) ( z = 0.49 ), (c) ( z = 0.21 ), and (d) ( z = 1.87 ).
(a) the area to the right of ( z = 0.82 ) is
(round to four decimal places as needed.)

Explanation:

Step1: Recall the formula for area to the right

The area to the right of \(Z = z\) is \(P(Z>z)=1 - P(Z\leq z)\).

Step2: Find \(P(Z\leq0.82)\) using standard normal table

From the standard - normal table (or using a calculator with a normal - distribution function, for example, in Excel: =NORM.S.DIST(0.82,TRUE)), \(P(Z\leq0.82)=0.7939\).

Step3: Calculate \(P(Z > 0.82)\)

\(P(Z>0.82)=1 - P(Z\leq0.82)=1 - 0.7939\).

Answer:

\(0.2061\)