Binomial Mean and Variance

The formula for the MEAN of a BINOMIAL DISTRIBUTION.

• np

• np(1-p)

• pq

• nx

Given n=10, p=0.9, and q=0.1. Compute the MEAN.

• 9

• 1

• 0.9

• 0.1

Find the variance of a binomial distribution with 50 trials and p= 0.4

• 12

• 15

• 10

• 20

It is known that about 90% of widgets made by Buckley Industries meet specifications. Every hour a sample of 18 widgets is selected at random for testing and the number of widgets that meet specifications is recorded. What is the approximate mean and standard deviation of the number of widgets meeting specifications?

• μ=1.62; σ=1.414

• μ=1.62; σ=1.265

• μ=16.2; σ=1.62

• μ=16.2; σ=1.273

Calculate the mean of a binomial distribution with n=10 and p=0.3.

• 0.5

• 15

• 7

• 3

Find the mean of a binomial distribution with n=50 and p=0.4

• 50

• 4

• 20

• 10

• Mean = 5.5 
  Variance =  1.57
  Standard Deviation = 2.475
• Mean = 5.0 
  Variance = 5.5
  Standard Deviation = 2.345
• Mean = 10
  Variance = .55
  Standard Deviation = .45
• Mean = 5.5 
  Variance = 2.475 
  Standard Deviation = 1.57 

• Mean =7.92
  Variance =  2.6928
  Standard Deviation = 1.64
• Mean = 12 
  Variance = .66
  Standard Deviation = .44
• Mean = 12
  Variance = 7.92
  Standard Deviation = 2.814
• Mean =7.92
  Variance = 1.64
  Standard Deviation = 2.6928 

• Not a binomial experiment
• Yes. n = 8
  p = .85 
  q = .15
   x = 0, 1, 2, 3, 4, 5, 6, 7, 8
• Yes. n = 8
  p = .15 
  q = .85
   x = 0, 1, 2, 3, 4, 5, 6, 7, 8
• Yes. n = 8
  p = .85 
  q = .15
   x = 8

• Not a binomial experiment
• Yes. n = 3
  p = 5/20 = .25 
  q = 15/20 = .75 
  x = 1, 2, 3 
• Yes. n = 3 
  p = 15/20 = .75 
  q = 5/20 = .25 
  x = 0, 1, 2, 3 
• Yes. n = 3
  p = 5/20 = .25
  q = 15/20 = .75
  x = 0, 1, 2, 3