Probability Distribution of Occupational Category

Questions: (a) Find the frequency distribution for the Occupational category (1=Management, 2=Sales, 3=Clerical, 4=Service, 5=Professional, 6=Other). Use Excel to produce a Descriptive Statistics table for your sample Occupational category data and paste into your MS Word assignment document. (b) Use the relative frequency approach to find the probability distribution for the Occupational category. (c) Draw the bar chart for the probability distribution of Occupational category. (d) Define the probability distribution based on part (b). x 1 2 3 4 5 6 P(x) 0.14 0.26 0.3 0.15 0.08 0.07 (e) Based on the probability distribution calculate the following i. Find the probability of exactly two ii. Find the probability more than two iii. Find the probability at least three. Answers: a. There are 6 categories of occupation. From our sample of size 60 that has been obtained, we obtain the frequency distribution of occupation as shown below. OCCUPATION Count 6 60 Thus, we observe that in the given sample, all the people belong to the occupational category Others. b. Relative frequency is a good approach to compute the probability of an event. Suppose the frequency of an event is f and the total frequency is n. Then the relative frequency of the event is (frequency of the event)/(Total frequency) =f/n. In this case, we have only one occupational category and its relative frequency = frequency/60 =60/60 =1 Thus the probability distribution of occupational category is shown below: OCCUPATION Count Probability 6 60 1 c. The bar chart for the probability distribution of Occupational category is given below: In the above diagram, 1 actually denotes Occupational Category 6 and all the samples units belong to the category Others. d. Considering the entire population, let X denote the Occupational Category of a person. Then X can take the values 1, 2, 3, 4, 5 and 6. According to our data given in task 1, we have a random sample of size 50 from the population and the corresponding probabilities of X are calculated according to the relative frequency method. For example P(X=1) = (number of people with Occupational Category 1)/50 In this way we compute all the probabilities for other values of X and the probability distribution table is shown below: X 1 2 3 4 5 6 P(x) 0.1 0.18 0.26 0.24 0.02 0.2 i. Based on the probability distribution given in the above probability distribution table, we compute some of the probabilities ii. Probability of exactly two =P(X=2) =0.18 (given in the above table) iii. Probability of more than two =P(X2) =P(X=3) + P(X=4) + P(X=5) +P(X=6) =0.26+0.24+0.02+0.2 =0.72 Probability of atleast three =P(X=3) =P(X=3) + P(X=4) + P(X=5) +P(X=6) =0.26+0.24+0.02+0.2 =0.72