A manufacturer claims that their light bulbs have an average life span that follows a normal distribution

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A manufacturer claims that their light bulbs have an average life span that follows a normal distribution with μ = 1,200 hours and a standard deviation of σ = 25.

If you randomly test 36 light bulbs and find that their average life span is X¯ = 1,150, does a .95 confidence interval for μ suggest that the claim μ = 1,200 is reasonable?

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