Unformatted text preview: 59/. .1? Assignment: Week 5 Exercises Date: 9/2471 1" Course: Math 201 Fall B10
Time: 3:12 PM Book: Larson: Elementary Statistics:
Picturing the World, 5c The heights of fully grown trees of a speciﬁc species are normally distributed, with a mean of 69.5 feet and a
standard deviation of 5.75 feet. Random samples of size 16 are drawn ﬁom the population. Use the central limit
theorem to ﬁnd the mean and standard error of the sampling distribution. Then sketch a graph of the sampling
distribution. The central limit theorem states that if the population itself is normally distributed, the sampling distribution of
sample means is normally distributed for any sample size n. The mean and standard error of the sampling
distribution (also called the standard error of the mean) are found using the formulas below. Since it; = u, the mean of the sampling distribution is the same as the population mean. Therefore, u; = 69.5 . 6
Use the formula 6; = V——- to ﬁnd the sample standard error.
5.75 W =1.44.~ l 1 Recall that the graph of the normal distribution is symmetric about the mean and has a spread deﬁned by the
standard deviation. Choose the correct graph of the sampling distribution below. M mam... WW“»%
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5%.": (35%.? 59,; ”251% "324 YOU ANSWERED: l Page 1 ...
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