Mathematics AI HL
IB Questions
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Question 1 of 2
A researcher records the number of correct answers (\(x\)) on a standardized test for a sample of IB Mathematics students.
\({x}\) | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|
Frequency | 4 | 8 | 20 | 18 | 9 | 2 |
Frequency distribution of test scores
Calculate an unbiased estimate of the population mean of \(x\).
Calculate an unbiased estimate of the population variance of \(x\).
The national average score on this test is 5.1. The researcher wants to test if IB Mathematics students perform better than the national average.
Given that \(H_0: \mu = 5.1\) is the null hypothesis for this test:
State the alternative hypothesis.
Perform an appropriate hypothesis test at the 5% significance level. State and justify your conclusion.
Question 2 of 2
In this question, you will explore possible approaches to using historical sports results for making predictions about future basketball matches.
Two students, Maria and John, are discussing ways of predicting the outcomes of NBA matches involving the Los Angeles Lakers.
Maria suggests analyzing historical data to help make predictions. She lists the results of the most recent 200 matches in which the Lakers played, in chronological order, then considers blocks of five matches at a time. She counts how many times the Lakers won in each block.
Number of wins for Lakers (per block of five matches) | Frequency |
---|---|
0 | 2 |
1 | 8 |
2 | 12 |
3 | 10 |
4 | 6 |
5 | 2 |
Frequency distribution table
Calculate the mean number of wins per block of five matches for the Lakers.
Maria thinks that this data can be modeled by a binomial distribution with \(n=5\) and decides to carry out a \(\chi^2\) goodness of fit test.
Calculate Maria's estimate for the probability \(p\) for this binomial model.
Calculate the probability that the Lakers win exactly three matches in their next block of five matches, using Maria's binomial model.