STAT207 Business Data Analysis Assignment

QUESTION 1

Below is the dataset for children enrolment in preschool or preschool program for 2021 across the different states in Australia.

1. Which measure of central tendency can be applied appropriately to the dataset presented above? Provide a reasonable justification for your response. 2 marks
2. Determine the standard deviation for (i) 4-year-olds enrolled in preschool or preschool program (no.) and (ii) 5-year-olds enrolled in preschool or preschool program (no.) and comment on their implications for each distribution. 4 marks
3. What social economic inference can be drawn from the descriptive statistic determine in (b) regarding children enrolment in preschool or preschool program across Australia? 4 marks

QUESTION 2

In a statistics class consisting of 120 students, it has been established that 1 in 20 students are likely to obtain a high distinction score in the final examination based on past records.

Required:

1. Discuss two key attributes of the above distribution that can be used for its identification and specify the type of distribution. 3 marks
2. Determine the probability that exactly five (5) students will obtain a high distinction score in the final examination. 2 marks
3. A new teaching assistant has been employed to facilitate the teaching and learning of statistics for current semester. She claims that 11 students will obtain a high distinction score in the final examination. Is her assertion valid? 3 marks

QUESTION 3

With the recent hikes in interest rates by the Reserve Bank of Australia, most consumers in Australia have attempted to promptly pay off their credit card bills. An analysis of the payment trend of consumers suggests that the payment trends are normally distributed with a mean amount of $130 and a standard deviation of $45.

1. What proportion of consumers are likely to pay at least $270 of their credit card bills? 2 marks
2. What proportion of consumers are likely to pay between $70 and $250. 4 marks
3. Is it possible for a consumer to pay more than $280 of their credit card bill? Explain your answer.

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