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2. Consider a normal distribution with a mean of 5 and a standard deviation of 0.75. Use this to find Q1, Q2, and Q3. 3. Consider a normal distribution with a mean of 17 and a standard deviation of 2. What is the z- score for x=18? 4. The longevity of MathBeats headphones is normally distributed with a mean of 5.2 years and a standard deviation of 1.1 years. (Longevity, in this case, is the amount of time these headphones function until they break.) (a) What is the probability that your headphones last at least 6 years? Include a sketch of this situation on an appropriately labeled bell-curve. (b) MathBeats includes a 3-year warranty on all of their headphones. They will replace any headphones that break before the 3 year mark with a new set. What is the probability that you will need this warranty? Include a sketch of this situation on an appropriately labeled bell curve.

2. Consider a normal distribution with a mean of 5 and a standard deviation of 0.75. Use this to find Q1, Q2, and Q3. 3. Consider a normal distribution with a mean of 17 and a standard deviation of 2. What is the z- score for x=18? 4. The longevity of MathBeats headphones is normally distributed with a mean of 5.2 years and a standard deviation of 1.1 years. (Longevity, in this case, is the amount of time these headphones function until they break.) (a) What is the probability that your headphones last at least 6 years? Include a sketch of this situation on an appropriately labeled bell-curve. (b) MathBeats includes a 3-year warranty on all of their headphones. They will replace any headphones that break before the 3 year mark with a new set. What is the probability that you will need this warranty? Include a sketch of this situation on an appropriately labeled bell curve.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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Part 2. The Central Limit Theorem 1. Recently, your college surveyed 100 students across campus and found that the mean age of students taking calculus is 23. (Suppose the standard deviation is 2.01 years.) (a) Explain why we can assume that the distribution is approximately normal. (b) What are the mean and standard deviation for the sample mean ages of calculus students? (c) Find the 90th percentile for the mean age of calculus students. Round to 1 decimal place. (d) Find the probability that a calculus student is younger than 18. (e) Is it unusual for a calculus student to be a minor? Explain your answer.
Transcribed Image Text:Part 2. The Central Limit Theorem 1. Recently, your college surveyed 100 students across campus and found that the mean age of students taking calculus is 23. (Suppose the standard deviation is 2.01 years.) (a) Explain why we can assume that the distribution is approximately normal. (b) What are the mean and standard deviation for the sample mean ages of calculus students? (c) Find the 90th percentile for the mean age of calculus students. Round to 1 decimal place. (d) Find the probability that a calculus student is younger than 18. (e) Is it unusual for a calculus student to be a minor? Explain your answer.
Lab 6- The Normal Distribution Part 1. The Normal Distribution 1. What does a z-score measure? Z-score indicates how much a given value difference from the standard deviation. The Z score, or standard score, is the number of standard deviations a given data point lies above or below the mean. 2. Consider a normal distribution with a mean of 5 and a standard deviation of 0.75. Use this to find Q1, Q2, and Q3. 3. Consider a normal distribution with a mean of 17 and a standard deviation of 2. What is the z- score for x=18? 4. The longevity of MathBeats headphones is normally distributed with a mean of 5.2 years and a standard deviation of 1.1 years. (Longevity, in this case, is the amount of time these headphones function until they break.) (a) What is the probability that your headphones last at least 6 years? Include a sketch of this situation on an appropriately labeled bell-curve. (b) MathBeats includes a 3-year warranty on all of their headphones. They will replace any headphones that break before the 3 year mark with a new set. What is the probability that you will need this warranty? Include a sketch of this situation on an appropriately labeled bell curve.
Transcribed Image Text:Lab 6- The Normal Distribution Part 1. The Normal Distribution 1. What does a z-score measure? Z-score indicates how much a given value difference from the standard deviation. The Z score, or standard score, is the number of standard deviations a given data point lies above or below the mean. 2. Consider a normal distribution with a mean of 5 and a standard deviation of 0.75. Use this to find Q1, Q2, and Q3. 3. Consider a normal distribution with a mean of 17 and a standard deviation of 2. What is the z- score for x=18? 4. The longevity of MathBeats headphones is normally distributed with a mean of 5.2 years and a standard deviation of 1.1 years. (Longevity, in this case, is the amount of time these headphones function until they break.) (a) What is the probability that your headphones last at least 6 years? Include a sketch of this situation on an appropriately labeled bell-curve. (b) MathBeats includes a 3-year warranty on all of their headphones. They will replace any headphones that break before the 3 year mark with a new set. What is the probability that you will need this warranty? Include a sketch of this situation on an appropriately labeled bell curve.
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