Question

use this table or the aleks calculator to complete the following. give your answers to four decimal places (for example, 0.1234). (a) find the area under the standard normal curve to the right of ( z = - 1.06 ). (b) find the area under the standard normal curve between ( z = - 2.46 ) and ( z = - 1.03 ).

Explanation:

Step1: Find area to the right of \( z = - 1.06 \)

The area to the right of \( z=-1.06 \) is \( P(Z>-1.06) = 1 - P(Z\leq - 1.06) \). Using the standard normal table or calculator, \( P(Z\leq - 1.06)=0.1446 \). So \( 1 - 0.1446=0.8554 \).

Step2: Find area between \( z=-2.46 \) and \( z = - 1.03 \)

The area between \( z=-2.46 \) and \( z=-1.03 \) is \( P(-2.46<Z<-1.03)=P(Z < - 1.03)-P(Z < - 2.46) \). Using the standard normal table or calculator, \( P(Z < - 1.03)=0.1515 \), \( P(Z < - 2.46)=0.0069 \). So \( 0.1515 - 0.0069 = 0.1446 \).

Answer:

(a) \( 0.8554 \)
(b) \( 0.1446 \)