Question

In Exercises 16 and 17, find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank.

16. About _______% of the area is between z = -0.75 and z = 0.75 (or within 0.75 standard deviations of the mean).

17. About _______% of the area is between z = -1.5 and z = 1.5 (or within 1.5 standard deviations of the mean).

Answer 1

16)

We have to find P( - 0.75 < Z < 0.75)

P( - 0.75 < Z < 0.75) = P(Z < 0.75) - P(Z < - 0.75) = 0.7734 - 0.2266 = 0.5467

( From z table)

About 54.67% of the area is between z = -0.75 and z = 0.75 (or within 0.75 standard deviations of the mean).

17)

We have to find P( - 1.5 < Z < 1.5)

P( - 1.5 < Z < 1.5) = P(Z < 1.5) - P(Z < - 1.5) = 0.9332 - 0.0668 = 0.8664

About 86.64% of the area is between z = -1.5 and z = 1.5 (or within 1.5 standard deviations of the mean).