Module 7: The Central Limit Theorem
Section Exercises
Barbara Illowsky & OpenStax et al.
The Central Limit Theorem for Sample Means (Averages)
- In words, Χ = ____________
- Χ ~ _____(_____,_____)
- In words,[latex]displaystyleoverline{{X}}[/latex]= ____________
- [latex]displaystyleoverline{{X}}[/latex]~ ______ (______, ______)
- Find the probability that an individual had between $0.80 and $1.00. Graph the situation, and shade in the area to be determined.
- Find the probability that the average of the 25 students was between $0.80 and $1.00. Graph the situation, and shade in the area to be determined.
- Explain why there is a difference in part e and part f.
- If[latex]displaystyleoverline{{X}}[/latex] = average distance in feet for 49 fly balls, then[latex]displaystyleoverline{{X}}[/latex] ~ _______(_______,_______)
- What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for[latex]displaystyleoverline{{X}}[/latex]. Shade the region corresponding to the probability. Find the probability.
- Find the 80th percentile of the distribution of the average of 49 fly balls.
- In words, Χ = _____________
- In words,[latex]displaystyleoverline{{X}}[/latex]= _____________
- [latex]displaystyleoverline{{X}}[/latex] ~ _____(_____,_____)
- Would you be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours? Explain why or why not in complete sentences.
- Would you be surprised if one taxpayer finished his or her Form 1040 in more than 12 hours? In a complete sentence, explain why.
- [latex]displaystyleoverline{{X}}[/latex] ~ _____(_____,_____)
- Find the probability that the runner will average between 142 and 146 minutes in these 49 marathons.
- Find the 80th percentile for the average of these 49 marathons.
- Find the median of the average running times.
- In words, Χ = _________
- Χ ~ _____________
- In words,[latex]displaystyleoverline{{X}}[/latex] = _____________
- [latex]displaystyleoverline{{X}}[/latex] ~ _____(_____,_____)
- Find the first quartile for the average song length.
- The IQR(interquartile range) for the average song length is from _______–_______.
- In words, Χ = _____________
- In words,[latex]displaystyleoverline{{X}}[/latex] = _____________
- [latex]displaystyleoverline{{X}}[/latex]~ _____(_____,_____)
- The IQR for[latex]displaystyleoverline{{X}}[/latex] is from _______ acres to _______ acres.
- When the sample size is large, the mean of[latex]displaystyleoverline{{X}}[/latex] is approximately equal to the mean of Χ.
- When the sample size is large,[latex]displaystyleoverline{{X}}[/latex] is approximately normally distributed.
- When the sample size is large, the standard deviation of[latex]displaystyleoverline{{X}}[/latex] is approximately the same as the standard deviation of Χ.
- [latex]displaystyleoverline{{X}}[/latex] ~ ______(______, ______)
- For the group of 16, find the probability that the average percent of fat ca