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.

Problem 12BSC

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(-1.07 < z < 0.67)

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

= P(z < 0.67) - P(z < -1.07)

area under normal curve can be calculated by using standard normal table or statistical table that is P(z < 0.67) = 0.7486 (i.e, row 0.6 under column 0.07)

P(z < -1.07) = 0.1423 (i.e, row -1.0 under column 0.07)

consider,

P(-1.07 < z < 0.67) = P(z < 0.67) - P(z < -1.07)

= 0.7486 - 0.1423

= 0.6063.

Therefore, the area of the shaded region is 0.6063.