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zysi [14]
3 years ago
5

IQ is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Fin

d the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ greater than 95) = ________ % b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ less than 125) = ___________% c) In a sample of 500 people, how many people would have an IQ less than 110? d) In a sample of 500 people, how many people would have an IQ greater than 140? people
Mathematics
1 answer:
nasty-shy [4]3 years ago
3 0

Answer:

Step-by-step explanation:

Let X be the IQ

IQ is normally distributed with a mean of 100 and a standard deviation of 15.

a) the probability that this person has an IQ greater than 95

=P(X\geq 95)\\=P(Z\geq \frac{95-100}{15} \\=P(Z\geq -0.33)\\=0.1293+0.5\\=0.6293

=62.93%

b) the probability that this person has an IQ less than 125

=P(X\leq 125) =P(X\leq 1.67)\\=0.5-0.4525\\=0.0475

=4.75%

c) Sample size =500

P(X

No of people = 0.2486(500) =124.3

d) P(x>140)\\= P(Z>2.6)\\=0.5-0.4953\\=0.0047

No of persons = 0.0047(500) = 2.35

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