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Question 6

From Math Applications HL Paper 1 (May 2025, TZ2)

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  1. [Maximum mark: 5]

The temperatures at 5 different locations on a coral reef were measured. The mean of this sample was 20.1°C and the standard deviation of this sample, sns_n, was 3.2°C.

(a) Find an unbiased estimate of the population variance. [2]

(b) Assuming that the temperatures are normally distributed, find a 95% confidence interval for the mean temperature on the coral reef. [2]

(c) Using your answer to part (b), determine if it is plausible that the mean temperature on the coral reef could be 17°C. [1]