A population of scores forms a normal distribution with a mean
of μ = 71 and a standard deviation of σ =
11.
(a) What proportion of the scores in the population have values
less than X = 69? (Round your answer to four decimal
places.)
(b) If samples of size n = 8 are selected from the
population, what proportion of the samples will have means less
than M = 69? (Round your answer to four decimal
places.)
(c) If samples of size n = 31 are selected from the
population, what proportion of the samples will have means less
than M = 69? (Round your answer to four decimal
places.)
Let the random variable X denote the scores.Given that X~ N(71,11)
(a) Standardizing X,
Using standard normal tables,
We get,
P(X<69) = P(Z<-0.18) = 0.4286 = 42.86%
Proportion of the scores in the population that would have values less than X = 69 is 0.4286
(b) If n = 8,
0.3050 = 30.5%
Proportion of the samples that would have means less than M = 69 is 0.3050
(c) For n = 31,
%
Proportion of the samples that would have means less than M = 69 is 0.1562
A population of scores forms a normal distribution with a mean of μ = 71 and...
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