Lifespan: Assume the average life-span of those born in the U.S. is 78.2 years w

Question

Lifespan: Assume the average life-span of those born in the U.S. is 78.2 years with a standard deviation of 16 years. The distribution is not normal (it is skewed left). The good people at Live-Longer-USA (fictitious) claim that their regiment of acorns and exercise results in longer life. So far, 50 people on this program have died and the mean age-of-death was 85.1 years. (a) Calculate the probability that a random sample of 50 people from the general population would have a mean age-of-death greater than 85.1 years. Round your answer to 4 decimal places.

Explanation / Answer

Lifespan: Assume the average life-span of those born in the U.S. is 78.2 years with a standard deviation of 16 years. The distribution is not normal (it is skewed left). The good people at Live-Longer-USA (fictitious) claim that their regiment of acorns and exercise results in longer life. So far, 50 people on this program have died and the mean age-of-death was 85.1 years. (a) Calculate the probability that a random sample of 50 people from the general population would have a mean age-of-death greater than 85.1 years. Round your answer to 4 decimal places.

Since sample size 50 is larger ( > 30), by central limit theorem, sample mean follows approximately normal distribution.

Standard error = sd/sqrt(n) =16/sqrt(50) =2.2627

Z value of 85.1, z=(85.1-78.2)/2.2627 = 3.05

P( mean x >85.1)

=P( z >3.05)

=0.0011

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