MATH 225N Week 6 Assignment; Confidence Intervals-Empirical Rule
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Course
MATH 225N (MATH225N)
Institution
Chamberlain College Of Nursing
1. Question: The average number of onions needed to make French onion soup from a population of recipes is unknown. A random sample of recipes yields a sample mean of x¯=8.2 onions. Assume the sampling distribution of the mean has a standard deviation of σx¯=2.3 onions.
Use the Empirical Rule t...
Confidence Intervals – Empirical Rule
Week 6
1. The average number of onions needed to make French onion soup from a
population of recipes is unknown. A random sample of recipes yields a
sample mean of x¯=8.2 onions. Assume the sampling distribution of the
mean has a standard deviation of σx¯=2.3 onions.
Use the Empirical Rule to construct a 95% confidence interval for the true
population mean number of onions.
(x¯−z⋅σx¯,x¯+z⋅σx¯)(8.2−2⋅2.3,8.2+2⋅2.3)(8.2−4.6,8.2+4.6)
(3.6,12.8)
2. In a random sample of 30 young bears, the average weight at the age of breeding is
312 pounds. Assuming the population ages are normally distributed with a population
standard deviation is 30 pounds, use the Empirical Rule to construct a 68% confidence
interval for the population average of young bears at the age of breeding. Do not round
intermediate calculations. Round only the final answer to the nearest pound. Remember to
enter the smaller value first, then the larger number. (307,317)
3. A random sample of garter snakes were measured and the proportion of
snakes that were longer than 20 inches in length recorded. The
measurements resulted in a sample proportion of p′=0.25, with a sampling
standard deviation of σp′=0.05.
Write a 68% confidence interval for the true proportion of garter snakes
that are over 20 inches in length (p′−z⋅σp′,p′+z⋅σp′)
(0.25−1⋅0.05,0.25+1⋅0.05)(0.25−0.05,0.25+0.05)
(0.20,0.30)
4. The average height of a population is unknown. A random sample from
the population yields a sample mean of x¯=66.3 inches. Assume the
sampling distribution of the mean has a standard deviation of σx¯=0.8
inches.
Use the Empirical Rule to construct a 95% confidence interval for the true
population mean height.
= (64.7, 67.9)
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