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IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If a certain statistician has an IQ of 122, what percent of the population has an IQ less than she does?


A. 7%
B. 22%
C. 93%
D. 99%
E. 47%

Respuesta :

HomertheGenius
z = ( 122-100 ) / 15 = 22/15 = 1.467
Then we have to use a z-table for a normal distribution.
The percent of the population that has an IQ less than she does is C ) 93%

Answer:

93% of the population has an IQ less than she does

Step-by-step explanation:

Mean = [tex]\mu = 100[/tex]

Standard deviation = [tex]\sigma = 15[/tex]

x = 122

Formula : [tex]z= \frac{x-\mu}{\sigma}[/tex]

[tex]z= \frac{122-100}{15}[/tex]

[tex]z=1.46[/tex]

Refer the z table for p value

So, p value = 0.9279

Percentage = 92.7% ≈ 93%

So, 93% of the population has an IQ less than she does

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