Question: 6. A multiple choice test has 20 questions, each with four possible answers. If students randomly guessed on every question the average number of questions

6. A multiple choice test has 20 questions, each with four possible answers. If students randomly guessed on every question the average number of questions answered correctly would be 5 with a standard deviation of 1.94. If this Binomial distribution is approximated with a normal curve what percentage of students would pass this test by randomly guessing on every question? (3 marks)

7. Using the statistics provided for the average annual income per person for 100 countries from aroung the world in 2022. (10 marks)

a) Determine the mean and sample standard deviation for the data set.

b) Hungary has an average annual income of $8613, what percentile does this place Hungary in?

c) make a relative histogram and frequence polygon for the data using

d) Hungary's average income is the 68th highest of the 100 countries listed. What percentile does this actually place them in?

e) Give reasons why the answers in parts b) and d) don't match

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