Continuous Distributions Notes
Continuous 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
b) What is the probability that it takes less than 20 minutes to drive to school?
c) What is the mean and standard deviation of this distribution?
Normal Distributions
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:
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?
Standard Normal Density Curves
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?
What proportion of these batteries can be expected to last more than 220 hours?
How long must a battery last to be in the top 5%?
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.
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
Normal Scores
Are these approximately normally distributed?
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