I\'m a study done on the life expectancy of 500 people in a certain geographic r

Question

I'm a study done on the life expectancy of 500 people in a certain geographic region, the mean age at death was 72 years and the standard deviation was 5.3 years.

2. In a study done on the life expectancy of 500 people in a certain geographic region, the mean age at death was 72 years and the standard deviation was 5.3 years. (a) What is the probability that an individual selected at random will be less than 70 years old? (b) What is the probability that an individual selected at random will be more than 70 years old? (c) If a sample of 50 people from this region is selected, find the probability that the mean life expectancy will be more than 70 years. (d) 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.

Explanation / Answer

Mean is 72 and s is 5.3

z can be found as (x-mean)/s

a) P(x<70)= P(z<(70-72)/5.3)=P(z<-0.38) or 1-P(z<0.38). from normal distribution table we get 1-0.6480 =0.352

b) P(x>70)=1-P(x<70)=1-0.352 =0.6480

c) P(xbar>70) =P(z>(70-72)/(5.3/sqrt(50)))=P(z>-2.67)=P(z<2.67). hence from normal distribution table we get 0.9962

d) This is 1-0.9962=0.0038

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