Question

1. A local historian knows that the age of artifacts in his library is Normally distributed with an average of 76 years old with a standard deviation of 14 years.

(a) Determine the probability a randomly selected artifact has an age over 90 years old.

(b) Determine the probability that the average of 2 randomly selected artifacts has an age over 90 years old.

(c) Determine the probability that the average of 3 randomly selected artifacts has an age over 90 years old.

(d) Determine the probability that the average of 4 randomly selected artifacts has an age over 90 years old.

(e) Determine the probability that the average of 10 randomly selected artifacts has an age over 90 years old.

(f) Determine the probability that the average of 15 randomly selected artifacts has an age over 90 years old.

Answer 1

a)

P(x>90)
= P(z> (90-76)/14)
= P(z>1)
= 0.1587

b)
n = 2

P(x>90)
= P(z> (90-76)/(14/sqrt(2))
= P(z>1.4142)
= 0.0787

c)
n = 3

P(x>90)
= P(z> (90-76)/(14/sqrt(3))
= P(z>1.7321)
= 0.0416

d)
n = 4

P(x>90)
= P(z> (90-76)/(14/sqrt(4))
= P(z>2)
= 0.0228

e)

n = 10

P(x>90)
= P(z> (90-76)/(14/sqrt(10))
= P(z>3.1623)
= 0.0008

f)
n =15

P(x>90)
= P(z> (90-76)/(14/sqrt(15))
= P(z>3.8730)
= 0.0001