#### III. C. Continuous Probability Distributions

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III. C. Continuous Probability Distributions

Example
Find the following probabilities:
P Z 1.9
P Z 0.4
P 2.3 Z 0.6
Example
A machine dispenses popcorn into ‘12 oz.’ packages. The
weight follows a normal probability distribution with a
mean of 12 oz. with a standard deviation of 0.6 oz.
What does the empirical rule tell you about this data?
What percentages of packages will have a weight less
than 11 oz?
What is the probability a randomly selected package
will have a weight greater than 11 oz?
What is the proportion of packages with a weight
between 11 and 12 oz?
Example
The life of a certain type of motor is normally distributed
with a mean of 10 years, with a standard deviation of
2 years.
What percentage of motors will have a life of less than
14.5 years?
What percentage of motors will have a life greater than
12.5 years?
What percentage of motors will have a life between 7
years and 9 years?
If the manufacturer is willing to replace 3% of motors
that fail, how long a guarantee should they offer?