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 0.2061
(round to four decimal places as needed.)
(b) the area to the right of ( z = 0.49 ) is 0.3121
(round to four decimal places as needed.)
(c) the area to the right of ( z = 0.21 ) is
(round to four decimal places as needed.)

Explanation:

Step1: Use the standard normal distribution property

The total area under the standard normal curve is \(1\). The area to the right of \(Z = z\) is \(1-\Phi(z)\), where \(\Phi(z)\) is the cumulative - distribution function of the standard normal distribution.

Step2: Find \(\Phi(0.21)\)

Looking up the value of \(Z = 0.21\) in the standard - normal table (or using a calculator with a normal - distribution function, e.g., in Excel: NORM.S.DIST(0.21, TRUE)).
From the standard - normal table, \(\Phi(0.21)=0.5832\)

Step3: Calculate the area to the right

Using the formula \(A = 1-\Phi(z)\), substitute \(z = 0.21\). Then \(A=1 - 0.5832=0.4168\)

Answer:

\(0.4168\)