Assume that iq scores are normally distributed with a mean of 100 and a standard deviation of 16. if 100 people are randomly selected, find the probability that their mean iq score is greater than 103. (rounded to the four decimal places)

0.03 is  the probability that for the sample mean IQ score is greater than 103.      

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 16

Sample size, n = 100

We are given that the distribution of IQ score is a bell shaped distribution that is a normal distribution.

Formula:

Standard error due to sampling =

P( mean IQ score is greater than 103)

P(x > 103)

Calculation the value from standard normal z table, we have,  

0.03 is  the probability that for the sample mean IQ score is greater than 103.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: