Question

The quality management division of a company that manufactures tires requires the average diameter of a certain model tire to be 36 inches, and the standard deviation of the diameters to be .2 inches. Assuming the distribution is normal:

a) Within what range would you expect 95% of the tires to fall.

b) What diameters on tires would be considered outliers?

c) What is the probability that a tire would have diameter less than 35.95 inches?

d) What is the probability that a tire would have diameter between 35.95 and 36.05 inches?

e) What is the probability that a tire would have diameter of 36 inches?

f) If a sample of size 43 is to be taken from this population of tires, what is the value of the sample mean?

g) If a sample of size 43 is to be taken from this population of tires, what is the value of the standard error of the mean

Answer 1

mean = 36 and sd = 0.2

a)
z-value = 1.96
lower bound = 36 - 1.96*0.2 = 35.6080
upper bound = 36 + 1.96*0.2 = 36.3920

b)
diameters less than 35.6080 and greater than 36.3920 are considered outliers

c)
P(X < 35.95)
=P(z < (35.95 - 36)/0.2)
= P(z < -0.2500)
= 0.4013

d)
required probabiltiy = 1-2*0.4013 = 0.1974

e)
probailtiy = 0

f)
sample mean = 36

g)
se = 0.2/sqrt(43) = 0.0305