)A normally distributed population has mean 25.6 and standard deviation 3.3
(a) Find the probability that a single randomly selected element X of the
population exceeds 30.
(b)Find the mean and standard deviation of X¯ for samples of size 9.
(C)Find the probability that the mean of a sample of size 99 drawn from this
population exceeds 30.
a) mean=25.6, sd=3.3
P(X>30)
Z="\\frac{X-\\mu} {\\sigma}"
="\\frac{30-25.6}{3.3}" =1.33
P(z>1.33)=0.09176 from the z tables.
=0.09176
b) mean of "\\bar X"
"\\mu=\\bar X=25.6"
Standard deviation
"s=\\frac{\\sigma} {\\sqrt n}"
="\\frac {3.3}{\\sqrt 9}" =1.1
c) P(X>30) given n=99
Z="\\frac{30-25.6}{\\frac{3.3}{\\sqrt{99}}}" =13.27
P(z>13.27)"\\approx" 0 from the standard normal tables.
=0
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