Answer :
The probability that the sample mean would be less than 20876 dollars is 0.0320.
P (x< 20876)
= P (z< (x -mean)/(sigma/sqrt(n))
= P (z < (20876 - 21053)/(805/sqrt (71))
= P (z < -1.85)
= 0.0320
As per binomial distribution,
P(X=r) = nCr * p^r * (1-p) ^(n-r)
P (x< 5) = 8C0 * 0.4^0 * (1-0.4) ^8 + 8C1 * 0.4^1* (1-0.4)^7 + 8C2 * 0.4^2 * (1-0.4)^6 + 8C3 * 0.4^3 * (1-0.4)^5 + 8C4 * 0.4^4 * (1-0.4)^4
P (x< 5) = 0.8263
P(x<28455)
= P (z< (x -mean)/(sigma/sqrt(n))
= P (z< (28455 - 28631)/ (4103.0001/sqrt (178))
= P (z< -0.57
= 0.2836
Per capita income (PCI) or total income measures the average profits earned according to individual in a given location (metropolis, vicinity, U.S.A , and so forth.) in a detailed yr. it's far calculated by means of dividing the vicinity's general earnings by using its general population. per capita profits are countrywide income divided by way of population length. per capita income is frequently used to degree a region's common income and evaluate the wealth of various populations. per capita income is likewise regularly used to degree a country's fashionable of living.
Additionally, it is expressed in terms of a typically used global foreign money together with the euro or U.S. dollar, and is useful because it's far widely known, is without difficulty calculable from without difficulty to be had gross domestic product (GDP) and population estimates and produces a beneficial statistic for contrast of wealth between sovereign territories. This facilitates to ascertain a country's improvement status. it's far one of the three measures for calculating the Human improvement Index of a rustic. Average income is another name for per capita income.
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