Empirical knowledge asserts that the IQ score X of people is normally distributed with mean defined to be =100 and standard deviation o = 15. (a) Which of the following random variables, follow the standard normal distribution N(0, 1)? X-15 (i) 100 X+ 15 (ii) X- 100 (izi) 100 15 100 X + 100 X+ 100 (iv) (vi) 15 225 225

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give  answer as a decimal number with five decimal digits.

 Find the probability a randomly selected person to have IQ:

(c) Find the probability a randomly selected person to be of IQ between 106 and 115.
d) Find the probability a randomly selected person to be of IQ between 91 and 115.
(e) Anna's IQ is higher than the 97.5% of the people. What is Anna's IQ (to one decimal place)?
(f) The 12.1% of the people have IQ higher than Mary. What is Mary's IQ (to two decimal places)?
Transcribed Image Text:(c) Find the probability a randomly selected person to be of IQ between 106 and 115. d) Find the probability a randomly selected person to be of IQ between 91 and 115. (e) Anna's IQ is higher than the 97.5% of the people. What is Anna's IQ (to one decimal place)? (f) The 12.1% of the people have IQ higher than Mary. What is Mary's IQ (to two decimal places)?
Empirical knowledge asserts that the IQ score X of people is normally distributed with mean defined to be
=100 and standard deviation o =
= 15.
(a) Which of the following random variables, follow the standard normal distribution N(0, 1)?
X-15
X+ 15
(ii)
100
X-100
(i)
100
(iiz)
15
100
(u)
X+100
X+100
(iv)
225
(vi)
15
225
Transcribed Image Text:Empirical knowledge asserts that the IQ score X of people is normally distributed with mean defined to be =100 and standard deviation o = = 15. (a) Which of the following random variables, follow the standard normal distribution N(0, 1)? X-15 X+ 15 (ii) 100 X-100 (i) 100 (iiz) 15 100 (u) X+100 X+100 (iv) 225 (vi) 15 225
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