Distributions In a continuous uniform distribution, μ = minimum + maximum 2 and σ = range 12 a. Find the mean and standard deviation for the distribution of the wailing times represented in Figure 6-2, which accompanies Exercises 5-8. b. For a continuous uniform distribution with μ = 0 and σ = 1, the minimum is − 3 and the maximum is 3 . For this continuous uniform distribution, find the probability of randomly selecting a value between −1 and 1, and compare it to the value that would be obtained by incorrectly treating the distribution as a standard normal distribution . Does the distribution affect the results very much?
Distributions In a continuous uniform distribution, μ = minimum + maximum 2 and σ = range 12 a. Find the mean and standard deviation for the distribution of the wailing times represented in Figure 6-2, which accompanies Exercises 5-8. b. For a continuous uniform distribution with μ = 0 and σ = 1, the minimum is − 3 and the maximum is 3 . For this continuous uniform distribution, find the probability of randomly selecting a value between −1 and 1, and compare it to the value that would be obtained by incorrectly treating the distribution as a standard normal distribution . Does the distribution affect the results very much?
Solution Summary: The author explains that the mean and standard deviation of waiting times are 2.5 minutes and 1.4 minutes respectively.
Distributions In a continuous uniform distribution,
μ
=
minimum + maximum
2
and
σ
=
range
12
a. Find the mean and standard deviation for the distribution of the wailing times represented in Figure 6-2, which accompanies Exercises 5-8.
b. For a continuous uniform distribution with μ = 0 and σ = 1, the minimum is −
3
and the maximum is
3
. For this continuous uniform distribution, find the probability of randomly selecting a value between −1 and 1, and compare it to the value that would be obtained by incorrectly treating the distribution as a standard normal distribution. Does the distribution affect the results very much?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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