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2.5.5 Hypothesis test for the mean of a normal distribution (A-level only)

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Question 17

The lifespan of a certain brand of light bulb is normally distributed with a mean of 1200 hours and a standard deviation of 80 hours.

a.

Find the probability that a randomly selected light bulb lasts for less than 1050 hours.

[2]
b.

An engineer claims that the manufacturing process has changed, causing the mean lifespan to decrease.

State the engineer's null and alternative hypotheses.

[1]
c.

A sample of 30 light bulbs is tested and the mean lifespan is found to be 1175 hours.

Carry out a test at the 10% significance level to determine if there is evidence that the mean lifespan is less than 1200 hours.

[3]

2.5.5 Hypothesis test for the mean of a normal distribution (A-level only) Questions

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  3. /2.5.5 Hypothesis test for the mean of a normal distribution (A-level only)