Advanced level 2025 Littoral Regional Mock mathematics statistics 3
Advanced level 2025 Littoral Regional Mock mathematics statistics 3
| (ii) at most two arc faulty. | (2 marks) |
| The probability that a box of n bulbs contains none that is faulty is less than 0.1. Find the range of possible | |
| values of n. (b) Over a period, the number of serious road accidents in a particular city averages 2 per day. Find, to four decimal places , the probability that (i) there is no accident on a given day, (ii) there are more than 2 accidents on a given day, (iii) there arc fewer than 3 accidents in three consecutive days. |
(3 marks) |
6.
(a) Explain the following as used in significance testing:
(i) level of significance
(ii) critical region
(iii) one–tailed and two–tailed tests.
(b) A student claims that 60 % of the population of a certain school Union are ready to vote for him as the
president of the union. A random sample of 2500 voters shows that 1450 support him. Test this claim at
the 1 % level of significance.
(c) A sample of size 64 with a mean weight of 100 kg and a standard deviation of 40 kg is drawn from
a population.
Estimate, at the 99 % level of confidence, the population mean based on the sample mean
20 % of the students in a certain high school have Mathematics textbooks.
A random sample of 400 students is selected from the high school.
(i) Determine the mean and variance of the number of students having mathematics text books.
Use the normal distribution as an approximation to the Binomial distribution to find, to four decimal
places, the probability that out of these 400 students,
(ii) at least 75 are in possession of the Mathematics text books,
(iii) between 65 and 95 students arc in possession of Mathematics textbooks,
(iv) exactly 90 students are in possession of the required textbooks.
(1 mark)
Cakes produced by students during the youth week in one school were graded on 20 by two Food and nutrition
teachers as follows:
8.
Class FI A FIB F2A F2B F3A F3B F4Arts F4SC F5Arts F5Sc
Teacher I (x) 16 15 9 13 17 19 18 17 12 15
Teacher 2 (y) 18 8 15 15 18 16 16 14 13
Calculate to three decimal places the Pearson Product moment correlation coefficient and comment
on your answer.
(ii) Find the equation of the least squares regression line of y on x.
A student of F2A was scored 14 by Teacher 1 was not scored by Teachers 2
(iii) Estimate the mark they would have earned from Teacher 2.
(iv) Calculate the minimum sum of squares of residuals of the marks awarded by teacher 1 on marks
awarded by teacher 2.
