Inferential Statistics Exercises - University of Western Australia

Inferential Statistics Exercises

These exercises have been written to consolidate your understanding of the Inferential Statistics workshop.

Question 1

State whether each of the following are valid probability distributions. If it is valid, state the expected value. If it is not valid, say why.

(a)

Outcome 1 2 3 4 5 Probability 0.1 0.2 0.3 0.2 0.2

(b)

Outcome 1 2 3 4 5 Probability 0.1 -0.2 0.7 0.2 0.2

(c)

Outcome 2 10 6 0 8 Probability 0.5 0.1 0.1 0.1 0.1

(d)

Outcome 0 -2 -3 4 -5 Probability 0.2 0 0.4 0.2 0.2

(e)

Outcome -3 1 -5 2 3 Probability 0.1 0.2 0.5 0.2 0.1

(f )

Outcome 0 1 2 3 4 Probability 1/2 1/4 1/8 1/16 1/32

(g)

Outcome 1 2 3 4 5 Probability 1/3 0 1/6 1/6 1/6

(h)

Outcome 1 2 3 4 5 Probability 0 1 0 0 0

Question 2

Assume that the weights of a population of rabbits is normally distributed with a mean of 7kg and a standard deviation of 2kg.

(a) Estimate the weight of the heaviest rabbit. (b) Estimate the weight of the lightest rabbit. (c) Calculate the probability that a randomly selected rabbit weighs between 5kg and 9kg.

(d) Calculate the probability that a randomly selected rabbit weighs between 3kg and 9kg.

(e) Calculate the probability that a randomly selected rabbit weighs between 3kg and 5kg.

Question 3 Assume that the arm-span of a population of humans is normally distributed with a

mean of 1.7m and a standard deviation of 10cm.

(a) Calculate the probability that a randomly selected human has an arm-span between 170cm and 180cm

(b) Calculate the probability that a randomly selected human has an arm-span of exactly 170cm.

(c) Calculate the probability that a randomly selected human has an arm-span of less than 150cm.

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