Question

A study investigating the relationship between age and annual medical expenses randomly samples 100 individuals in a city. It is hoped that the sample will have a similar mean age as the entire population. Complete parts a and b below.

a. If the standard deviation of the ages of all individuals in the city is σ=15​, find the probability that the mean age of the individuals sampled is within two years of the mean age for all individuals in the city.​ (Hint: Find the sampling distribution of the sample mean age and use the central limit theorem. You​ don't have to know the population mean to answer​ this, but if it makes it​ easier, use a value such as μ=25​.)

The probability is... (Round to three decimal places as​ needed.)

b. Would the probability be​ larger, or​ smaller, if σ=5​? Why?If σ were smaller​,the standard deviation of the sampling distribution would be (smaller, larger), so the probability would be (larger, smaller).

Answer 1

Pgno O Answer:- Griven that, n=100 standard Error of mean (56) = 15 3100 115 By central limit theorem, sample mean (X) N (4, 1.5 Z=x-u probability: Ply-d <x<lt2) = P(-2<zu<2) =P(-03 x-M =P(-1.33 <7<1:33) = P(Z<133) - P(Z2-1:33) 0.9082 - 010917 0.8165 i probability 0.8165 b Co 5 562 GIELL - 015 XNN(40.5

Pgno @ Z = X-M 015 : Pl_2<x-M<d) ) =P(-4< X-4 <4) Pla <X-4 0.5 015 =P(-49.0< Z <mpo) = PLZ24) - P(Z<-4) - 1-0 probability = 1 The standard deviation would be smaller of Sampling distribution the probability would be larger