The 20 to 34 age groups are approximately normally distributed with µ = 110

21.94% of people aged 20 to 34 have IQs between 125 and 150.

Step-by-step explanation:

The complete question is: Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20 to 34 age group are approximately Normally distributed with  μ = 110  and  σ = 25.

What percent of people aged 20 to 34 have IQs between 125 and 150?

Let X = Scores on the standard IQ test for the 20 to 34 age group

SO, X ~ Normal()

The z-score probability distribution for the normal distribution is given by;

                            Z  =    ~ N(0,1)

where, = population mean = 110

            = standard deviation = 25

Now, the percent of people aged 20 to 34 have IQs between 125 and 150 is given by = P(125 < X < 150) = P(X < 150) - P(X 125)

       P(X < 150) = P( < ) = P(Z < 1.60) = 0.9452

       P(X 125) = P( ) = P(Z 0.60) = 0.7258

The above probability is calculated by looking at the value of x = 1.60 and x = 0.60 which has an area of 0.9452 and 0.7258.

Therefore, P(125 < X < 150) = 0.9452 - 0.7258 = 0.2194 or 21.94%

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .