1e was $3735 with a samp 4. In a ran fuel cost are d deviation of $607. Construc

Question

1e was $3735 with a samp 4. In a ran fuel cost are d deviation of $607. Construct the 998 confidence interval for the annua population normally distributed. mean. Interpret the result. Assume that mean is 5. The average weight of adult male inhabitants of the town of Kilomoto normally distributed with a mean of 135 pounds and a standard deviation of 12.6 pounds. (Please show all work) a. Find the mean and standard deviation of the sampling distribution of sample means. Please round to two (2) decimal places when necessary b. If 45 inhabitants of kilomoto are selected at random, what is the probability that they will have a mean that is greater than 137.5 pounds ? c. If 45 inhabitants are selected at random, what is the probability that they will not be within 5 pounds of the mean?

Explanation / Answer

5.

Mean=135
Stdev=12.6
N=45

a. Sample' mean is same as population mean = 135
Sample' standard deviation is = stdev of pop. /sqrt(n) = 12.6/sqrt(45)= 1.88

b.P(Xbar>137.5) = P(Z> 137.5-135 / 12.6) = P(Z>.198) = 1-.5793 = .4207

c.P(not within 5 pounds)
= 1-P( within 5 pounds of mean)
= 1-P(130<X<140)
= 1-P(130-135/12.6<Z<140-135/12.6)
= 1-P(-.397<X<.397)
= 1-(.654-.346 )
= .692

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