FizeauV

2021-08-19

Based on the Normal model N(100, 16) describing IQ scores, what percent of peoples

Sadie Eaton

Skilled2021-08-20Added 104 answers

1. The distribution of IQ scores is normally distributed with a mean of 100 and a standard deviation of 16.

2. Transform the normal random variable,X, into the standard normal variable Z by using the following formula:

a)

b)

c)

Jeffrey Jordon

Expert2021-10-06Added 2605 answers

The percentage needed is for the area shown here :

Let us suppose the number corresponding to the needed percentage is X, we get the following expression:

P(X>80)

Knowing that

So, in the next steps , we will get the Z value from X and calculate its percentage as follows:

P(X >80)

=1-0.1056=0.8944

Therefore, 89.44% of people's IQs would be over 80

b)The percentage to be calculated is for the following colored area:

P(X<90)

=0.266

Therefore, 26.6% of people's IQs would be under 80

c)The percentage to be calculated represents the data within the covered area:

P(112<X<132)

=0.2039

Therefore, 20.39% of people's IQs would be between 112 and 132

Jazz Frenia

Skilled2023-06-12Added 106 answers

fudzisako

Skilled2023-06-12Added 105 answers

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