Assume that IQ is normally distributed, with mean 100 and standard deviation 15.

ID: 3126755 • Letter: A

Question

(a) What is the probability that a randomly selected per- sons IQ is over 120?

(b) Find the values of Q1, Q2, and Q3 for IQ.

(c) Find the values of lower = Q1 1.5(Q3 Q1) and upper = Q3 + 1.5(Q3 Q1) for IQ. Recall that these were cutoffs for outliers.

(d) Find the probability of an outlier for IQ for a single person based on your values for (c).

(e) If we randomly selected 10 people, what is the prob- ability their average IQ is over 105?

(a)For x=120,

Z=(x-)/=(120-100)/15=1.33

Thus, P(x>120)=P(z>1.33)=1-P(z<1.33)=1-0.9082=0.0918

(b) For the first quartile, say, q1, and the area to the left is .25.

From the standard normal table it has been found that z=-0.67

Thus, q1=-0.67*+=-0.67*15+100=89.95

Similarly, q3=+0.67*15+100=110.05

(c)Q1-1.5(Q3-Q1)=89.95-1.5(110.05-89.95)

=59.8

Q3+1.5(Q3-Q1)=110.5+1.5(110.05-89.95)

=140.2

(e)If 10 people are selected then the mean is 100 and standard deviation 15/sq rt10=4.74

For x=105, z=(105-100)/4.74=1.05

P(z>1.05)=0.1469

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.