Transcript sect4-4 - Gordon State College

Section 4-4
Mean, Variance, and Standard
Deviation for the Binomial
Distribution
MEAN, VARIANCE, AND
STANDARD DEVIATION
• The mean or expected value for the binomial
distribution is
μ=n·p
• The variance for the binomial distribution is
σ2 = n · p · q = n · p · (1 − p)
• The standard deviation for the binomial
distribution is
  n  p  q  n  p  (1  p)
MINIMUM AND MAXIMUM
USUAL VALUES
Recall:
minimum usual value = μ − 2σ
maximum usual value = μ + 2σ
EXAMPLES
1. According to Nielson Media Research, 75%
of all United States households have cable
television. In a simple random sample of
300 households, determine the mean and
standard deviation of households that will
have cable television.
2. Suppose in a simple random sample of 300
households 244 have cable television. Is this
result unusual?