The probabilities that a local police department receives 10, 11, 12, 13, and 14 emergency calls per 24-hour period are 0.02, 0.12, 0.40, 0.31, and 0.15, respectively. Construct a probability distribution. Find the mean, variance, and standard deviation of the distribution.
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Answer:
The probability distribution of a binomial random variable is called a binomial distribution. ... The mean of the distribution (μx) is equal to n * P . The variance (σ2x) is n * P * ( 1 - P ). The standard deviation (σx) is sqrt[ n * P * ( 1 - P ) ].The probabilities that a local police department receives 10, 11, 12, 13, and 14 emergency calls per 24-hour period are 0.02, 0.12, 0.40, 0.31, and 0.15, respectively. Construct a probability distribution. Find the mean, variance, and standard deviation of the distribution.SOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions
1. The following table contains a probability distribution for a random variable X.
x 1 2 3 4 5
P(x) 0.16 0.22 0.28 0.20 0.14
a. Find the expected value (mean) of X.
x P(x) xP(x)
1 0.16 0.16
2 0.22 0.44
3 0.28 0.84
4 0.20 0.80
5 0.14 0.70
ΣP(x) = 1 ΣxP(x) = 2.94
µ = 2.94