Question

Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a

mean of 100 and a standard deviation of 15.
Click to view page 1 of the table. Click to view page 2 of the table
120
The area of the shaded region is
(Round to four decimal places as needed.)

Answer 1

The area of the shaded region is 0.9525

As per given information,

Mean = μ = 100,

standard deviation = σ = 15

The cumulative probability of z = 1.67 is 0.9525, which can be seen in the standard normal table with z values of 1.6 in the row and 0.07 in the column.

To the area of the shaded region.

P(X < 125) =
`p((x-\mu)/(\sigma)` )

P(X < 125) = P (
`(125 -100)/(25)`)

P(z < 1.67) = 0.9525

Answer 2

1. 0.7475

2. 0.6997

3. x = 110.1175

The given information are:

mean = 100

standard deviation = 15

Formula in use: P(X < B) = P( (B - mean)/(standard deviation) )

1

P(X<110) = P(Z< (110-100)/15) =P(Z< 2/3) = 0.7475

2

P(90<X<125) = P(125) - P(90) = P(Z< (125-100)/15) - P(Z< (90 - 100)/15) = P(Z< 5/3) - P(Z< -2/3) = 0.95221 - 0.25249 = 0.69972 = 0.6997

3

P(X< B) = area

((Z - 100)/15) = P^-1 (0.75)

(Z - 100)/15 = 0.6745

Z - 100 = 10.1175

Z = 10.1175 + 100 = 110.1175