ution 1Q is normally distributed with a mean of 100 and a standard deviation of

Question

ution 1Q is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Find the probability that this person has an 1Q 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 10 less than 125. Write your answer in percent form. Round to the nearest tenth of a percent c) In a sample of 500 people, how many people would have an 1Q less than 110? d) In a sample of 500 people, how many people would have an 1O greater than 140? P(lQ less than 125)- people Get help: Video Vidco Read Points possible: 1 This is attempt 1 of 3. 898 5 8 9 0

Explanation / Answer

solution :
Given that mean ? = 100 , standard deviation ? = 15

=> Here, x is the Iq

(a) P(x > 95) = P((x - ?)/? > (95 - 100)/15)
= P(Z > -0.3333)
= 0.6293
= 62.93%

(b) P(x < 125) = P((x - ?)/? < (125 - 100)/15)
= P(Z < 1.6667)
= 0.9525
= 95.25%

(c) n = 500,

P(x < 110) = P((x - ?)/(?/sqrt(n)) < (110 - 100)/(15/sqrt(500)))
= P(Z < 14.9071)
= 1

(d) n = 500,

P(x > 140) = P((x - ?)/(?/sqrt(n)) > (140 - 100)/(15/sqrt(500)))
= P(Z > 59.6285)
= 0

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