Sample Median and Sample Mean - Population Mean: - Mathematics Assignment Help

Assignment Task:

Task:

Question 1: (15 marks)

Answer the following short questions and give a reason to support your an- swer. Please note that no marks will be awarded if you do not provide a reason to support your answer.

(a) Give two situations in which you would recommend the sample median over the sample mean as a measure of location.

(b) Is the sample mean always larger than the sample median for skewed data?

(c) Is it true that histograms are a more effective graphical summary than boxplots when comparing two or more samples of data?

(d) Is it true that if B is a subset of A then P (A ∩ Bc ) = P (A) − P (Bc )?

(e) Is it true that discrete random variables always take integer or whole number values?

Question 2: (12 marks)

A skier is reported missing in a blizzard. The skier is either on slope A, slope B or slope C. The head of the rescue mission believes that the skier is on slope A with probability 0.5 and slope B with probability 0.3. Suppose that she has 12 rescue parties which are all equally competent and will locate the skier with probability 0.4 if they are on the correct slope. You may assume that the rescue parties work independently of each other. The head of the mission sends 6 rescue parties to slope A, four to slope B and 2 to slope C.

(a) If the missing skier is on slope A, what is the probability the missing skier will be rescued?

(b) If the missing skier is on slope B, what is the probability the missing skier will be rescued?

(c) If the missing skier is on slope C, what is the probability the missing skier will be rescued?

(d) What is the probability that the missing skier will be rescued?

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