4.15 Central limit theoremIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 4.15 Central limit theorem

1. The mass $X$ kg of a bag of flour is normally distributed with mean $1.00$ kg and standard deviation $0.04$ kg. A random sample of $9$ bags is taken, with masses independent of each other, and $\bar{X}$ is the mean mass of the sample.
   Explain why $\bar{X}$ is exactly normally distributed here, even though the sample size is only $9$.2 marks
2. The mass of an adult passenger, $X$ kg, is normally distributed with mean $78$ kg and standard deviation $11$ kg. Passenger masses are independent of each other.
   A lift is overloaded if the total mass of six passengers exceeds $500$ kg. Use your GDC to find the probability that the lift is overloaded.2 marks
3. The waiting time $T$ minutes of a caller at a call centre has mean $6.0$ minutes and standard deviation $4.5$ minutes. The distribution of $T$ is positively skewed, so it is not normal. A random sample of $50$ calls is taken and $\bar{T}$ is the mean waiting time of the sample.
   State the approximate distribution of $\bar{T}$, giving the reason why the approximation is valid and its parameters.3 marks