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On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 118 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.
b. Find the probability that a randomly selected person's IQ is over 115.

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Answer:

0.5675

Step-by-step explanation:

We have that, the IQ of the ruling species is normally distributed with a mean of 118 and a standard deviation of 18.

We want to find the probability that a randomly selected person's IQ is over 115.

We need to find the z-score of 115

using

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

We substitute x=115 to get:

[tex]z = \frac{115 - 118}{18} [/tex]

This implies that:

[tex]z = \frac{ - 3}{18} = - \frac{1}{6} = - 0.17[/tex]

We read from the normal distribution table to get;

P(X>115)=0.5675

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