Some iq tests are standardized to a normal model, with a mean of 100 and a standard deviation of 16.

a. what does the 68-95-99.7 rule predict?

b. about what percent of people should have iq scores above 84?

c. about what percent of people should have iq scores between 116 and 132?

d. about what percent of people should have iq scores below 68?

b) 84.1%

c) 13.5%

d) 2.35%                                

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 16

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

Formula:

a)  68-95-99.7 rule

b) percent of people should have IQ scores above 84

P(score greater than 84)

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

84.1% percent of people should have IQ scores above 84.

c)  percent of people should have IQ scores between 116 and 132

Thus, with the help of empirical rule, we can write,

13.5%  of people should have IQ scores between 116 and 132.

d) percent of people should have IQ scores below 68

P(IQ scores below 68)

P(x < 68)

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

2.35% of people should have IQ scores below 68.

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