Standard Normal Distribution. In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Equation Transcription:

Text Transcription:

z=-0.84

z=1.28

Problem 11BSC

Answer:

Step1 of 2:

We have In Exercises, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Step2 of 2:

From the above graph we have P(p < z <q ).

P(p < z <q ) = P(-0.84 < z < 1.28)

= P(z < q) - P(z < p)

= P(z < 1.28) - P(z < -0.84)

area under normal curve can be calculated by using standard normal table or statistical table that is P(z < 1.28) = 0.8997 (i.e, row 1.2 under column 0.08)

P(z < -0.84) = 0.2005 (i.e, row -0.8 under column 0.04)

consider,

P(-0.84 < z < 1.28) = P(z < 1.28) - P(z < -0.84)

= 0.8997 - 0.2005

= 0.6992.

Therefore, the area of the shaded region is 0.6992.