Download Continuous Distributions Notes

Continuous Distributions Notes
b) What is the probability that it takes less than 20
minutes to drive to school?
Continuous distribution –
c) What is the mean and standard deviation of this
distribution?
Density curves:
Uniform Distribution –
Formulas:
The Citrus Sugar Company packs sugar in bags
labeled 5 pounds. However, the packaging isn’t
perfect and the actual weights are uniformly
distributed with a mean of 4.98 pounds and a range
of .12 pounds.
a) Construct the uniform distribution above.
b) What is the probability that a randomly selected
bag will weigh more than 4.97 pounds?
c) Find the probability that a randomly selected bag
weighs between 4.93 and 5.03 pounds.
The time it takes for students to drive to school is
evenly distributed with a minimum of 5 minutes and
a range of 35 minutes.
a) Draw the distribution
Normal Distributions
Strategies for finding probabilities or proportions
in normal distributions
The lifetime of a certain type of battery is normally
distributed with a mean of 200 hours and a standard
deviation of 15 hours. What proportion of these
batteries can be expected to last less than 220 hours?
Do these two normal curves have the same mean? If
so, what is it?
Which normal curve has a standard deviation of 3?
Which normal curve has a standard deviation of 1?
Empirical Rule:
What proportion of these batteries can be expected
to last more than 220 hours?
Suppose that the height of male students at CHS is
normally distributed with a mean of 71 inches and
standard deviation of 2.5 inches. What is the
probability that the height of a randomly selected
male student is more than 73.5 inches?
How long must a battery last to be in the top 5%?
Standard Normal Density Curves
The heights of the female students at CHS are
normally distributed with a mean of 65 inches.
What is the standard deviation of this distribution if
18.5% of the female students are shorter than 63
inches?
The heights of female teachers at CSH are normally
distributed with mean of 65.5 inches and standard
deviation of 2.25 inches. The heights of male
teachers are normally distributed with mean of 70
inches and standard deviation of 2.5 inches.
Describe the distribution of differences of heights
(male – female) teachers.
Normal Scores
What is the probability that a randomly selected
male teacher is shorter than a randomly selected
female teacher?
Ways to Assess Normality
Normal Probability Plot
Are these approximately normally distributed?
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