DP Further Mathematics HL Questionbank

• Syllabus

3.4

Sub sections and their related questions

A linear combination of independent normal random variables is normally distributed. In particular, \(X{\text{ ~ N}}\left( {\mu ,{\sigma ^2}} \right) \Rightarrow \bar X{\text{ ~ N}}\left( {\mu ,\frac{{{\sigma ^2}}}{n}} \right)\) .

• 11M.1.hl.TZ0.1b: A random sample of size four is taken from the distribution N(60, 36) . Calculate the...
• 13M.1.hl.TZ0.5a: (i)     Find \({\rm{E}}(Y)\) in the form \(p\mu \) , where \(p \in \mathbb{R}\) . (ii)     Find...
• 07M.1.hl.TZ0.6a: (i)     Find the mean and variance of \(2Y - X\) . (ii)     Find the probability that the weight...
• 07M.1.hl.TZ0.6b: Two randomly chosen male birds and three randomly chosen female birds are placed together on a...
• 15M.1.hl.TZ0.7a: Sami is undertaking market research on packets of soap powder. He considers the brand “Gleam”....
• 15M.1.hl.TZ0.7b: Sami now considers the brand “Bright”. The weight of the contents of a randomly chosen packet of...
• 15M.1.hl.TZ0.14: Sarah is the quality control manager for the Stronger Steel Corporation which makes steel sheets....
• 15M.2.hl.TZ0.2a: State the distribution of \(\bar X\) , giving its mean and standard deviation.

The central limit theorem.

• 09M.2.hl.TZ0.1B.a: State and justify an appropriate test procedure giving the null and alternate hypotheses.
• 09M.2.hl.TZ0.1B.b: What is the critical region for the sample mean if the probability of a Type I error is to be...
• 09M.2.hl.TZ0.1B.c: If the mean weight of the bags is actually \(28\).1 kg, what would be the probability of a Type...
• 16M.2.hl.TZ0.2b: (i)     Find \({\text{E}}({X^2})\). (ii)     Show that \({\text{Var}}(X) = 2\).
• 16M.2.hl.TZ0.2c: State the central limit theorem.
• 16M.2.hl.TZ0.2d: Find the probability that the sample mean is less than 2.3.