4.16 Confidence intervalsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 4.16 Confidence intervals

1. The masses of cats of a certain breed are normally distributed with a known standard deviation of $0.6$ kg. A random sample of $25$ of these cats has a mean mass of $4.20$ kg. A confidence interval is to be found for the population mean mass $\mu$.
   The breed society claims that the mean mass of these cats is $4.5$ kg. Use your interval from (b) to comment on this claim.2 marks
2. The lifetimes, in hours, of a type of battery are normally distributed with unknown mean $\mu$ and unknown standard deviation. The lifetimes of a random sample of $12$ batteries are: $40.2,\ 38.9,\ 41.5,\ 39.8,\ 42.1,\ 40.7,\ 39.3,\ 41.0,\ 40.4,\ 38.6,\ 41.8,\ 40.2$. Use your GDC where helpful.
   Use your GDC to find a $95\%$ confidence interval for $\mu$.2 marks
3. The daily screen time of teenagers, in minutes, is normally distributed with a known standard deviation. A $95\%$ confidence interval for the population mean $\mu$, based on a random sample of $64$ teenagers, is $(152.65,\ 167.35)$.
   (i) Write down the sample mean. (ii) Find the value of the population standard deviation.3 marks