A laboratory tested 86 chicken eggs and found that the mean amount of cholesterol was x = 228 mg. Assume that the population standard deviation is known to be 19 mg. (a) Why are we allowed to assume that the sampling distribution in this problem is approximately normal? (Select the correct answer ) The margin of error is unknown. The population is normally distributed. The population standard deviation is known. The sample size is large enough. (b) Construct a 95% confidence interval for the true mean cholesterol content, ?, of all such eggs. Round your answers to two decimal places. lower limit upper limit margin of error (c) Interpret your results in the context of this problem. We can be 95% certain that the true mean cholesterol for the sample is inside the interval found in part (b). We can be 95% certain that the true mean cholesterol for the population is outside the interval found in part (b). We can be 95% certain that the true mean cholesterol for the sample is outside the interval found in part (b). We can be 95% certain that the true mean cholesterol for the population is inside the interval found in part (b). (d) Find the sample size necessary for an 95% confidence level with a maximal margin of error E = 2.5 for the mean cholesterol content. Round up to the nearest whole number.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A laboratory tested 86 chicken eggs and found that the mean amount of cholesterol was x = 228 mg. Assume that the population standard deviation is known to be 19 mg.

(a) Why are we allowed to assume that the sampling distribution in this problem is approximately normal? (Select the correct answer )

The margin of error is unknown.

The population is normally distributed.

The population standard deviation is known.

The sample size is large enough.

(b) Construct a 95% confidence interval for the true mean cholesterol content, ?, of all such eggs. Round your answers to two decimal places.

lower limit
upper limit
margin of error

We can be 95% certain that the true mean cholesterol for the sample is inside the interval found in part (b).

We can be 95% certain that the true mean cholesterol for the population is outside the interval found in part (b).

We can be 95% certain that the true mean cholesterol for the sample is outside the interval found in part (b).

We can be 95% certain that the true mean cholesterol for the population is inside the interval found in part (b).

(d) Find the sample size necessary for an 95% confidence level with a maximal margin of error E = 2.5 for the mean cholesterol content. Round up to the nearest whole number.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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