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Scores on the Wechsler intelligence quotient (IQ) test for adults have a normal probability distribution with a mean score of 100 and a standard deviation of 15 points. The US military has minimum enlistment standards at about an IQ score of 85. Based on IQ scores only, what is the probability that a randomly selected adult does not meet US military enlistment standards

Respuesta :

Answer:

Probability = 0.1587

Step-by-step explanation:

The provided information is:

Let X be the scores of the IQ test for adults that is normally distributed with mean [tex](\mu)[/tex] = 100 and standard deviation [tex](\sigma)[/tex] = 15.

Also, US military has minimum IQ score of 85.

Thus, the probability that randomly selected adult does not meet US military enlistment standards is: [tex]P(X<85)[/tex]

The probability can also be written as:

[tex]P(X < x) =P(Z<\frac{x-\mu}{\sigma})[/tex]

Thus,

[tex]P(X<85)=P(Z<\frac{85-100}{15})\\\\=P(Z<-1)[/tex]

Using the Normal probability table probability of Z = -1 is 0.1587

Thus, the required probability is 0.1587

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