Advanced level 2025 North West Regional Mock mathematics statistics 1

Here is the extracted data from the image:

SECTION R: STATISTICS

36. Given that C and D are independent events, such that P(C)=43​ and P(D)=65​, then the value of P(C∩D) is:

A. 1211​

B. 85​

C. 125​

D. 83​

37. The mean of 40 numbers is 5. Ten numbers are selected from the population and the mean is 8. The mean of the remaining 30 numbers is:

A. 4

B. 380​

C. 0

D. 120

38. A discrete random variable X takes the values 2, 3 and 4 with probabilities 0.5, 0.2 and 0.3 respectively. The mean of X is:

A. 0.31

B. 2.8

C. 9

D. 2.9

39. In descriptive statistics, the true representative of a data is:

A. Mean

B. Cumulative

C. Variance

D. Mode

40. If A and B are two events such that P(A)=2/5, P(B)=2/3 and P(A∩B)=1/5, then A and B are:

A. Mutually exclusive

B. Exhaustive

C. Independent

D. Not exhaustive

41. A continuous random variable X has a probability density function f(x)=kx, where 0≤x≤2. The value of k is:

A. 1

B. 21​

C. 41​

D. 43​

43. Samples of size n are taken from a distribution whose variance is 64. If the standard error of the sample mean is 2, then the value of n is:

A. 4

B. 32

C. 64

D. 2

44. A vegetable producer in Santa sells vegetable in bags with stated weight of 25kg. A customer in the Bamenda food market claims that she is being cheated. A hypothesis test is to be conducted to confirm or reject her claim. The Null and Alternative hypothesis for this test will be stated as:

A. H0​:μ=25,H1​:μ<25

B. H0​:μ=25,H1​:μ>25

C. H0​:μ=25,H1​:μ=25

D. H0​:μ≤25,H1​:μ=25

45. Three pairs of ranks were made by two judges over such that ∑d2=2. The Spearman’s Rank correlation coefficient is:

A. 0.7

B. 0.9

C. 0.8

D. 0.6

46. A sample of four match boxes taken from the output of a filling machine has variance 6. The unbiased estimate for the variance is:

A. 6

B. 8

C. 2

D. 1

47. For a regression graph, the coordinate of the point where the two lines of regression, y on x and x on y will pass through is:

A. (xˉ,yˉ​)

B. (0,0)

C. (1,1)

D. (−1,−1)

48. Given that X∼N(150,4), P(147<X<155) is:

A. Φ(2.5)−Φ(−1.5)−1

B. Φ(2.5)+Φ(−1.5)

C. Φ(2.5)−Φ(−1.5)

D. Φ(2.5)+Φ(1.5)−1

49. A statistic is used to estimate a population parameter is known as:

A. Sample

B. Estimator

C. Variable

D. Constant