A particular population of deer mice is known to have mean body length of 86mm a

Question

A particular population of deer mice is known to have mean body length of 86mm and standard deviation 8mm. 3

(a) Describe the distribution of sample mean body lengths, for random samples of 36 deer mice (taken from the population).

(b) What can you say about the distribution of sample mean body lengths for samples of 10 deer mice?

(c) If we assume that the distribution of body lengths of deer mice in the population is normal, what is the probability that a sample of 10 mice has mean body length less than 80mm?

Explanation / Answer

a) here distribution of sample mean body lengths will be approximately normal with mean =86mm

and std error of the mean =std deviation/(n)1/2 =8/(36)1/2 =1.3333

b) similarly for sample size is less then 30 we can not be sure that distribution is normal/ but best estimate for mean =86

and std deviation=(8/(10)1/2)=2.5298

c) P(X<80)=P(Z<(80-86)/2.5298)=P(Z<-2.3717)=0.0089

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