The weight of a Dog is normally distributed with mean A kg and standard deviatio
ID: 3178691 • Letter: T
Question
The weight of a Dog is normally distributed with mean A kg and standard deviation 2.B. kg. (eg. If your B is 45 then standard deviation is 2.B = 2.45 Find The probability that a Dog is less than 35 kg The probability that a dog is greater than 32 kg What dog's weight would be at the start of the top 5% of the heaviest dogs. Interpret your answer. You sampled dogs 16 at a time and calculate the sample mean for the sample. What would the sample mean at the top (heaviest) 10% of sample means sampled in this way?Explanation / Answer
mean = 45
std. dev. = 2.45
(A)
P(X<35) = P(z<(35-45)/2.45) = P(z<-4.0816) = 0
(B)
P(X>32) = P(z<(32-45)/2.45) = P(z<-5.3061) = 1
(C)
For top 5%, z-value is 1.64
xbar = 45 + 1.64 * 2.45 = 49.018
Hence 49.018kg would be the weight at the start of the top 5% of the heaviest dogs.
(D)
For top 10%, z-value is 1.28
xbar = 45 + 1.28 * 2.45/sqrt(16) = 45.784
Hence 45.784 kg would be the sample mean at the top 10% of sample means sampled.
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