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natima [27]
3 years ago
15

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 105 and a standard deviation sigma equa

ls 15. Find the probability that a randomly selected adult has an IQ between 90 and 120.
Mathematics
2 answers:
kondor19780726 [428]3 years ago
5 0

Answer:   0.6827

Step-by-step explanation:

Given : Mean IQ score : \mu=105

Standard deviation : \sigma=15

We assume that adults have IQ scores that are normally distributed .

Let x be the random variable that represents the IQ score of adults .

z-score : z=\dfrac{x-\mu}{\sigma}

For x= 90

z=\dfrac{90-105}{15}\approx-1

For x= 120

z=\dfrac{120-105}{15}\approx1

By using the standard normal distribution table , we have

The p-value : P(90

P(z

Hence,  the probability that a randomly selected adult has an IQ between 90 and 120 =0.6827

zaharov [31]3 years ago
3 0

Answer:

Step-by-step explanation:

Let X be the IQ scores of adults

Given that X is normally distributed with a mean of mu equals 105 and a standard deviation sigma equals 15.

Thus Z score corresponding to any X would be

\frac{x-105}{15}\

Required probability

=probability that a randomly selected adult has an IQ between 90 and 120.

=P(90<X<120)

= P(-1<z<1)

= 0.6836

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