Question #345935

activity 2 solve the following problems. show all your works. 1 in a study of the life expectancy of 500 people in a certain geographic region, the mean age at death was 720 years, and the standard deviation was 5.3 years. if a sample of 50 people from this region is selected, find the probability that the mean life expectancy will be less than 70 years.

1
Expert's answer
2022-05-30T16:11:06-0400

Given μ=72.0\mu=72.0 years, σ=5.3\sigma=5.3 years, N=500,n=50.N=500, n=50.


σX=σnNnN1=5.3505005050010.7118\sigma_{X}=\dfrac{\sigma}{\sqrt{n}}\sqrt{\dfrac{N-n}{N-1}}=\dfrac{5.3}{\sqrt{50}}\sqrt{\dfrac{500-50}{500-1}}\approx0.7118

P(X<70)=P(Z<70720.7118)P(X<70)=P(Z<\dfrac{70-72}{0.7118})

P(Z<2.80985)0.0025\approx P(Z<-2.80985)\approx0.0025


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