An organization has members who possess IQs in the top 4% of the population. If IQs are normally distributed, with a mean of 100 and a standard deviation of 15, what is the minimum IQ required for admission into the organization?
• Use Excel, and round your answer to the nearest integer.
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SerenaBochenek SerenaBochenek · Answer 1 · 2020-10-22T08:00:13+02:00

Answer:

The minimum IQ score will be "126".

Step-by-step explanation:

The given values are:

Mean

[tex]\mu = 100[/tex]

Standard deviation

[tex]\sigma=15[/tex]

Now,

⇒ [tex]P(z>x)=4 \ percent \ i.e., 0.04[/tex]

⇒ [tex]P(z>\frac{x- \mu}{\sigma} )=0.04[/tex]

⇒ [tex]1-P(z \leq \frac{x-100}{15})=0.04[/tex]

⇒ [tex]\frac{x-100}{15}=z0.96[/tex]

[tex]=NORMDIS(z=0.96)[/tex]

[tex]=1.751[/tex]

⇒ [tex]x=100+15\times 1.751[/tex]

[tex]=126.265 \ i.e., 126[/tex]