The Australian sheep dog is a breed renowned for its inteligence and work ethic.
ID: 3056267 • Letter: T
Question
The Australian sheep dog is a breed renowned for its inteligence and work ethic. it is estimated that 30% of adult Australian sheep dogs weigh 65 pounds (Ib) or more. A sample of 40 adult dogs is studied and follow a binomial distribution. Let x be a binomial randome variable that represents the number of adult dogs in the sample who weigh 65 Ib or more (a) find the mean number of dogs in this sample who weigh 65 Ib or more (b) find the standard deviation of the number of dogs in the sample who weigh 65 Ib or more
Explanation / Answer
X ~ Binomial(n,p)
Where n = 40 , p = 0.30
a)
Mean = n * p
= 40 * 0.30
= 12
Mean = 12
b)
Standard deviation = Sqrt(n * p * (1-p) )
= Sqrt( 40 * 0.30 * 0.70)
= 2.8983
Standard deviation = 2.8983
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