Question

1. A population forms a normal distribution with a mean of µ = 120 and a standard deviation of σ = 14.

1. If two scores were selected from this population, how much distance would you expect, on average, between the second score and the population mean?

A sample of n = 20 scores from this population has a mean of M = 90, do you think this sample is relative typical or extreme to the population? Explain.

Answer 1

a.

for expected distance from mean we chech the z value that has P(z<Z) = 0.75

and P(z<-z) = 0.25 ,as we know for z=0 P(z<Z)=0.5 so for mean distance we check for equal probability differences in both sides

from table below we find : the required z = 0.67

therefore expected distance from mean =0.67*SD = 0.67*14

= 9.38

P(z<Z) table :

for sample of n=20 scores

SDsample = SD/(n^0.5) = 14/(20^0.5) = 3.1305

z = ((sample mean) - (population mean))/SD

so here z = (90-120)/3.1305

z-score = -9.5831

from the curve below we can see for z-score = -9.5831 the probability is extremely low

so, we can say this sample is extreme to the population

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