A-Level Maths: Statistics Practice

The data set {3, 5, 7, 8, 12} has values coded as y = (x - 8)/2. Find the mean of the coded values.

For the data set {2, 4, 4, 6, 8, 10}, find the standard deviation. Give your answer to 2 decimal places.

Find the interquartile range of the data set {3, 5, 7, 8, 9, 12, 14, 16, 18}.

Events A and B are such that P(A) = 0.4, P(B) = 0.5 and P(A|B) = 0.3. Find P(A ∪ B).

A bag contains 4 red and 6 blue balls. Two balls are drawn without replacement. Find the probability that both are the same colour.

In a group of 100 students, 40 study Maths, 35 study Physics, and 15 study both. A student is chosen at random. Given that they study Maths, what is the probability they also study Physics?

X ~ B(12, 0.3). Find P(X = 4).

A fair coin is tossed 10 times. Find the probability of getting exactly 7 heads.

The probability that a machine produces a defective item is 0.08. In a batch of 50 items, find the probability that at most 2 are defective.

Given X ~ N(μ, σ²) with μ = 50 and σ = 6, find P(X < 44).

The heights of adult males are normally distributed with mean 175 cm and standard deviation 8 cm. Find the probability that a randomly chosen male is taller than 185 cm.

X ~ N(100, 15²). Find the value of a such that P(X > a) = 0.05.

A coin is tossed 15 times and lands on heads 11 times. Test at the 5% significance level whether the coin is biased towards heads. State the critical region.

A manufacturer claims that the mean lifetime of batteries is 200 hours. A sample of 30 gives a mean of 192 hours with standard deviation 18 hours. Test at the 5% level whether the mean is less than 200 hours.

In a binomial hypothesis test with X ~ B(20, p₀) testing H₁: p > p₀, the critical value is found to be 7. What does this mean?

For a set of bivariate data, the product moment correlation coefficient (PMCC) is calculated as r = 0.85. What does this indicate about the relationship between the variables?

A regression line of y on x is given by y = 3.2x + 1.5. If x = 7, predict y and explain the limitation of this prediction.

In a Spearman's rank correlation test, rₛ = -0.72 and n = 10. Test at the 5% significance level whether there is a negative correlation. (Critical value at 5% for n=10 is 0.564)