#6 Suppose a random sample of n = 25 observations is selected from a population
ID: 3316246 • Letter: #
Question
#6 Suppose a random sample of n = 25 observations is selected from a population that is normally distributed with mean equal to 103 and standard deviation equal to 14.
(a) Give the mean and the standard deviation of the sampling distribution of the sample mean X.
(Enter your standard deviation to two decimal places.)
(b) Find the probability that x exceeds 110. (Round your answer to four decimal places.)
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(c) Find the probability that the sample mean deviates from the population mean = 103 by no more than 3. (Round your answer to four decimal places.)
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Explanation / Answer
A) mean of sampling distribution = 103
Standard deviation of sampling distribution = 14/sqrt(25) = 2.8
B) P(X > 110) = P(Z > (110 - 103)/14)
= P(Z > 0.5)
= 1 - P(Z < 0.5)
= 1 - 0.6915
= 0.3075
C) Probability = P(-3/2.8 < Z < 3/2.8)
= P(-1.07 < Z < 1.07)
= P(Z < 1.07) - P(Z < - 1.07)
= 0.8577 - 0.1423
= 0.7154
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