Advanced level 2026 North west regional mock mathematics with statistics 3
Advanced level 2026 North west regional mock mathematics with statistics 3
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(i) The number of voters arriving at a polling station follows a Poisson distribution with 5 voters in 20 minutes.
Calculate the probability that:
a) No voter will arrive between 3:10 and 3:30 pm
b) There will be exactly 5 voters between 9:20-10:20
(ii) A suitor searching for a Christian wife decides to attend church services in his church until he gets one.
Given that the probability of getting a wife up to and including the first success is $\frac{1}{5}$.
Calculate:
c) The mean and variance of the number of times he attends church service
d) The probability that he finds a wife on the $5^{th}$ church service
Find the least integer $n$, the number of times he attends church service such that $P(X > n) < 1\%$. (2, 4, 3, 2, 2 marks)
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(i) A random sample of 100 cabbages were harvested and weighed. The weights, $x$ grams are summarized by $\sum x = 16380$ and $\sum x^2 = 2,686,310$.
a) Calculate a 96% confidence interval for the mean weight of all cabbages.
b) What do you understand by “unbiased estimate of population variance”?
(ii) An infinite population consists of the numbers 1, 2, 3.
a) Write down the population mean of the sample.
b) Calculate the population variance.
Random samples of size 2 are obtained from the population.
c) Write down all possible samples of size 2 taken with replacement.
d) Obtain the expected value of the mean and the population variance. (4, 1, 2, 2, 2 Marks)
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(i) Define the following terms as used in hypothesis testing:
a) Test statistic
b) Acceptance region
c) Critical values
d) One-tailed test
(ii) The marks of a certain GCE paper were normally distributed with mean 42.3 and variance 125.44. As a practice examination 15 students from a particular school sat for the examination and their mean mark was 49.8.
Test, at the 1% level of significance, whether the students did better than the candidates in that GCE Paper. (1, 1, 1, 1, 9 Marks)
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The marks obtained by some 10 competitors in a cultural event are shown in the table below
| Competitor | A | B | C | D | E | F | G | H | I | J |
| Dancing(X) | 10 | 12 | 16 | 13 | 17 | 11 | 18 | 15 | 19 | 14 |
| Fashion Parade(Y) | 18 | 15 | 10 | 16 | 19 | 14 | 13 | 11 | 17 | 12 |
a) Calculate to 2 decimal places, the product-moment correlation coefficient between dancing marks and fashion parade marks.
b) Determine the least square regression line of the marks in fashion parade on the marks in dancing
c) Estimate the marks of a competitor in a fashion parade who fell ill but scored 19 marks in dancing. (8, 3, 2 Marks)
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