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## Statistics

problem 1: The file A1Q1.xls comprises of data for the percentage change in the price of 50 shares selected at arbitrary from the Australian Stock Exchange. The data refer to the percentage change in the share price between the start of trading and the close of trading on Friday 22nd February 2008.

i) Suppose that you had to purchase one of such shares as soon as trading commenced on that day and then sell it just before trading closed on that day. Which share would have given you the maximum return (yield) and which the lowest return?

ii) Use Excel to make a histogram of these data. Use upper-class limits (Excel’s Bins) of - 4, - 2.5, - 1, 0.5, 2, 3.5, 5, 6.5. Once you have the histogram, eliminate the gaps between the bars. (See SSK, p.48 &49)

iii) Is the histogram:

•    Symmetric
•    Positively skewed
•    Negatively skewed

iv) Use HISTOGRAM to ESTIMATE the proportion of shares with a negative return. [You are predictable to estimate the proportion of shares with a negative return by estimating the number of shares with returns less than 0. You might require estimating the proportion of negative returns in the class - 1 to 0.5].

v) Was it a good day to buy and sell shares?

problem 2:

The proportion of American Express credit-card holders who pay their credit card bill in full each and every month is 23%; the other 77% make only a part or no payment.

a) In a random sample of 15 customers, determine the probability that:

i) 4 customers pay their bill in full?
ii) More than 6 customers pay their bill in full?

b) In a random sample of 17 customers, determine the probability that:

i) 4 customers pay their bill in full?
ii) No more than 3 customers pay their bill in full?

problem 3:

“MagTek” electronics has developed a smart phone which does things that no other phone yet released into the market-place will do. The marketing department is planning to describe this new phone to a group of potential customers, however is worried regarding some initial technical problems which have resulted in 0.2% of all phones malfunctioning. The marketing executive is planning on arbitrarily selecting 60 phones for use in the explanation but is worried as it is very significant that every single one functions OK during the explanation. The executive believes that whether or not any one phone malfunctions is independent of whether or not any other phone malfunctions and is convinced that the probability that any one phone will malfunction is definitely 0.002. Supposing the marketing executive randomly chooses 60 phones for use in the demonstration:

a) Determine the probability that no phones will malfunction? [If you use any probability distribution/s, you are needed to justify the requirements for specific distributions are satisfied]

b) Determine the probability that at most one phone will malfunction?

c) The executive has decided that unless the probability of there being normal functions is more than 90%, he will cancel the demonstration. Should he cancel the explanation or not? Describe your answer.

problem 4:

Lifts generally have signs pointing out their maximum capacity. Consider a sign in a lift which reads ‘maximum capacity 1400kg or 20 persons’. Assume that the weights of lift-users are normally distributed with a mean of 65kg and a standard deviation of 10kg.

i) Determine the probability which a lift-user will weigh more than 70kg?

ii) Find out the probability that a lift-user will weigh between 60 and 75kg?

iii) Find out the probability that 20 people will exceed the weight limit of 1400kg?

iv) Determine the probability that 25 people will not surpass the weight limit (Use Excel to compute probability to 6 decimal places)?

Statistics and Probability, Statistics

• Category:- Statistics and Probability
• Reference No.:- M9587

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