Transcript Chapter 7 The Normal Probability Distribution

Chapter 7
The Normal Probability
Distribution
7.3
Applications of the Normal
Distribution
EXAMPLE Finding the Area Under a Normal
Curve
It is known that the length of a certain steel
rod is normally distributed with a mean of
100 cm and a standard deviation of 0.45
cm.* What is the probability that a randomly
selected steel rod has a length less than
99.2 cm?
*Based
upon information obtained from Stefan Wilk.
EXAMPLE Finding the Area Under a Normal
Curve
It is known that the length of a certain steel rod is
normally distributed with a mean of 100 cm and a
standard deviation of 0.45 cm. What is the
probability that a randomly selected steel rod has a
length between 99.8 and 100.3 cm?
EXAMPLE Finding the Area Under a Normal
Curve
It is known that the length of a certain steel rod is
normally distributed with a mean of 100 cm and a
standard deviation of 0.45 cm. Suppose the
manufacturer must discard all rods less than 99.1
cm or longer than 100.9 cm. What proportion of
rods must be discarded?
EXAMPLE
Finding the Area Under a Normal
Curve
It is known that the length of a certain steel rod is
normally distributed with a mean of 100 cm and a
standard deviation of 0.45 cm. Find the length
corresponding to the 35th percentile.
EXAMPLE
Finding the Area Under a Normal
Curve
It is known that the length of a certain steel rod is
normally distributed with a mean of 100 cm and a
standard deviation of 0.45 cm. Suppose the
manufacturer wants to accept 90% of all rods
manufactured. Determine the length of rods that
make up the middle 90% of all steel rods
manufactured.