Question

Assume the age of death for all us burials(of persons over 5 years old) is approximately normally distributed and the sample mean is 68.84 and the standard deviation is 18.402926789.

Find the age at death such that 1.5% of US burials (of persons over 5 years old) were at least that old.

Find the probability that a burial randomly selected from all US burials (of persons over 5 years old) involved a person at least 30 years old.

Find the probability that a burial randomly selected from all US burials ( of persons over 5 years old) involved a person at most 85 years old.

Answer 1

Here is step by step solution for the given problem. Hope this is useful.

Here it is given that the distribution of the age of death from US population is approximately normal, with a mean of 68.84 and standard deviation 18.402926789.

Consider X be the random variable denoting the age of death. Then X ~ N( 68.84, 18.402926789)

Then define       which is also Normally distributed with mean 0, and standard deviation 1. The cumulative probabilities for different values of Z are tabulated in the z-score tables, that are available in any standard statistical book, or the internet.

We find the required probabilities using Z.

a) To find x, such that P(X>x)=0.015

1.5% US burial were at least of age 108.77 approximately 109.

b) Here the criterion for age is at least 30 so we need the following probability:

i.e.

the probability that for a randomly selected burial the age of death was at least 30 is 98.26%

c) Here the criterion fro age is at most 85, i.e. death at 85 or younger than that. Here we need the following probability:

All the probability values or the z-values for the standard normal distribution are obtained using the z-score table.

i.e. the probability that a US burial randomly selected has the probability 81.01% of involving someone with age 85 or younger.