1) IQ is normally distributed with a mean of 100 and a standard deviation of 15.
ID: 2922036 • Letter: 1
Question
1) IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.
a) ive the distribution of X.
b) Find the probability that the person has an IQ greater than 140.
Write the probability statement. P (___)
What is the probability? (Round your answer to four decimal places.)
c) Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization.
Write the probability statement.
P(X > x) =
What is the minimum IQ? (Round your answer to the nearest whole number.)
x =
d) The middle 30% of IQs fall between what two values?
Write the probability statement.
P(x1 < X < x2) =
State the two values. (Round your answers to the nearest whole number.)
x1 = x2 =Explanation / Answer
NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 100
standard Deviation ( sd )= 15
a.
P(X > 140) = (140-100)/15
= 40/15 = 2.6667
= P ( Z >2.6667) From Standard Normal Table
= 0.0038
c.
P ( Z > x ) = 0.02
Value of z to the cumulative probability of 0.02 from normal table is 2.0537
P( x-u / (s.d) > x - 100/15) = 0.02
That is, ( x - 100/15) = 2.0537
--> x = 2.0537 * 15+100 = 130.8062
d.
P ( Z < x ) = 0.4
Value of z to the cumulative probability of 0.4 from normal table is -0.2533
P( x-u/s.d < x - 100/15 ) = 0.4
That is, ( x - 100/15 ) = -0.2533
--> x = -0.2533 * 15 + 100 = 96.1998
GREATER THAN
P ( Z > x ) = 0.4
Value of z to the cumulative probability of 0.4 from normal table is 0.2533
P( x-u / (s.d) > x - 100/15) = 0.4
That is, ( x - 100/15) = 0.2533
--> x = 0.2533 * 15+100 = 103.8002
P(x1 < X < x2) = P( 96.1998 < x < 103.8002) ~ P( 96 < x < 104)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.