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Probability Assignment

Probability Assignment

QUESTION 1 Probability Show all calculations/reasoning

Guide to marks: 18 marks – 4 for (a), 5 for (b), 6 for (c), 3 for (d)

(a)  Define what is meant by a probability distribution.

What is the difference between a discrete probability distribution and a continuous probability distribution?

Give an example of your own for each type of distribution.

(b)  Consider the following record of daily sales of a baker’s top selling loaf of bread over the last 100 days:

NUMBER SOLDNUMBER OF DAYS
05
115
220
325
420
515
Total100
  • What was the probability of selling 3 or 4 loaves on any one day?
  • What were the average daily sales over the period?
  • What was the probability of selling 2 or more loaves on any one day?
  • What was the probability of selling 4 loaves or less on any one day?

(c)  A coin is tossed twice. Calculate the probability of each of the following:

  • A head on the first toss.
  • A tail on the second toss given a head on the first toss
  • Two tails
  • A tail on the first toss and a head on the second toss
  • A tail on the first and a head on the second or a head on the first and a tail on the second
  • At least one head on the first two tosses

(d) The average sales of apples is 5000 with a standard deviation of 600.

  • What is the probability that sales will be greater than 5600 apples?
  • What is the probability that sales will be less than 5240 apples?
  • What is the probability that sales will be less than 4400 apples?

QUESTION 2 Research Question: Constructing data table and calculating probabilities

Guide to marks: 14 – 5 for 1, 5 for 2, 4 for 3

The following question involves learning/employing research skills in searching out data on the Internet, presenting it in a well constructed and informative table, and calculating some probabilities showing calculation methods.

  • Search the Internet for the latest figures you can find on the age and sex of the Australian population.
  • Then using Excel, prepare a table of population numbers (not percentages) by sex (in the columns) and age (in the rows). Break age into about 5 standard groups, eg, 0-14, 15-24, 25-54, 55-64, 65 and over. Insert total of each row and each column. Paste the table into Word as a picture.  Give the table a title, and below the table quote the source of the figures.
  • Calculate from the table, showing your calculation methods:
  • The probability that any person selected at random from the population is a male.
  • The probability that any person selected at random from the population is aged between 55 and 64.
  • The joint probability that any person selected at random from the population is a female and aged between 15 and 24.
  • The probability that any person selected at random from the population is 55 or over.
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