Week 4 Math Homework: Practice Questions and Insights

12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences… 1/10 Week 4 Knowledge Check Homework Practice Questions 1 2 Your work has been saved and submitted Written Dec 29, 2023 11:55 PM - Dec 30, 2023 12:35 AM • Attempt 1 of 4 Attempt Score 16 / 20 - 80 % Overall Grade (Highest Attempt) 16 / 20 - 80 % Question 1 1 / 1 point ___ 264.43___ Hide ques±on 1 feedback The length of a human pregnancy is normally distributed with a mean of 272 days with a standard deviation of 9 days (Bhat & Kushtagi, 2006). How many days would a pregnancy last for the shortest 20%? Round answer to 2 decimal places. Answer: In Excel, =NORM.INV(0.2,272,9)

12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences… 2/10 Question 2 0 / 1 point ___ 0.359___ (0.0359, .0359) Hide ques±on 2 feedback Question 3 1 / 1 point ___ 53.78___ Hide ques±on 3 feedback Question 4 0 / 1 point Which type of distribution does the graph illustrate? Find P(Z ≥ 1.8). Round answer to 4 decimal places. Answer: In Excel, =1-NORM.S.DIST(1.8,TRUE) The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt & Lunneryd, 2012). Assume the length of fish is normally distributed. What is the length in cm of the longest 15% of Atlantic cod in this area? Round answer to 2 decimal places. Answer: Longest 15% is the upper 85%, 1 - .15 = .85 In Excel, =NORM.INV(0.85,49.9,3.74)

12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences… 3/10 Question 5 1 / 1 point The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 26.3 mpg and a standard deviation of 11.2 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Answer: ___ Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate entry. Make sure you include the zero before the decimal. ___ Answer: 0.2029 Hide ques±on 5 feedback Left skewed Distribution Right Skewed Distribution Normal Distribution Uniform Distribution This is a sampling distribution problem with μ = 26.3. σ = 11.2, and sample size n = 30.

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12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences… 4/10 Question 6 1 / 1 point ___ 0.4966___ Hide ques±on 6 feedback Question 7 1 / 1 point ___ 0.314___ Hide ques±on 7 feedback Question 8 1 / 1 point The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution. The decay rate is: New SD = 11.2/SQRT(30) = 2.044831 P(x > 28) = 1 - NORM.DIST(28, 26.3, 2.044831, TRUE) The life of an electric component has an exponential distribution with a mean of 10 years. What is the probability that a randomly selected one such component has a life more than 7 years? Answer: (Round to 4 decimal places.) P(x > 7) 1-P(x < 7) =1-EXPON.DIST(7,1/10,TRUE) The commute time for people in a city has an exponential distribution with an average of 0.5 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours? Answer: (round to 3 decimal places) P(.4 < x < 1) P(x < 1) - P(x < .4) In Excel, =EXPON.DIST(1,1/0.5,TRUE)-EXPON.DIST(0.4,1/0.5,TRUE) 0.1666

12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences… 5/10 Hide ques±on 8 feedback Question 9 1 / 1 point The average lifetime of a set of tires is three years. The manufacturer will replace any set of tires failing within two years of the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that the tires will fail within two years of the date of purchase? Hide ques±on 9 feedback Question 10 1 / 1 point ___ 0.60___ Hide ques±on 10 feedback 0.6666 0.3333 0.5000 1/3 = .3333 0.8647 0.2212 0.4866 0.9997 P(x < 2) In Excel, =EXPON.DIST(2,1/3,TRUE) The waiting time for a train has a uniform distribution between 0 and 10 minutes. What is the probability that the waiting time for this train is more than 4 minutes on a given day? Answer: (Round to two decimal place.)

12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences… 6/10 Question 11 1 / 1 point ___ 0.9___ Hide ques±on 11 feedback Question 12 1 / 1 point ___ 0.75___ Hide ques±on 12 feedback Interval goes from 0 < x < 10 P(x > 4) = Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The probability that a random vehicle gets between 25 and 34 miles per gallon is: Answer: (Round to one decimal place) Interval goes from 25 < x < 35 P(25 < x < 34) = A local grocery delivery time has a uniform distribution over 0 to 60 minutes. What is the probability that the grocery delivery time is more than 15 minutes on a given day? Answer: (Round to 2 decimal places.) Interval goes from 0 < x < 60 P(x > 15) =

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12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences… 7/10 Question 13 1 / 1 point ___ 0.50___ Hide ques±on 13 feedback Question 14 0 / 1 point ___ 0.9___ (0.50, .50, .5, 0.5) Hide ques±on 14 feedback The waiting time for a bus has a uniform distribution between 0 and 10 minutes. What is the probability that the waiting time for this bus is less than 5 minutes on a given day? Answer: (Round to two decimal place.) Interval goes from 0 < x < 10 P(x < 5) = Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The probability that a random vehicle gets between 25 and 30 miles per gallon is: Answer: (Round to two decimal place) Interval goes from 25 < x < 35 P(25 < x < 30) =

12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences… 8/10 Question 15 1 / 1 point ___ 0.50___ Hide ques±on 15 feedback Question 16 0 / 1 point ___ 0.154___ (0.0154, .0154) Hide ques±on 16 feedback Question 17 1 / 1 point ___ 0.9515___ Hide ques±on 17 feedback Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The probability that a random vehicle gets between 28 and 33 miles per gallon is: Answer: (Round to two decimal place) Interval goes from 25 < x < 35 P(28 < x < 33) = The time a student sleeps per night has a distribution with mean 6.3 hours and a standard deviation of 0.6 hours. Find the probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night. Answer: (round to 4 decimal places) New SD = .6/SQRT(42) P(x > 6.5), in Excel =1-NORM.DIST(6.5,6.3,0.092582,TRUE) The final exam grade of a mathematics class has a skewed distribution with mean of 78 and standard deviation of 7.2. If a random sample of 38 students selected from this class, then what is the probability that the average final exam grade of this sample is between 75 and 80? Answer: (round to 4 decimal places)

12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences… 9/10 Question 18 1 / 1 point ___ 0.0038___ Hide ques±on 18 feedback Question 19 1 / 1 point ___ .9772___ Hide ques±on 19 feedback Question 20 1 / 1 point New SD = 7.2/SQRT(38) P(75 < x < 80), in Excel =NORM.DIST(80,78,1.1679943,TRUE)-NORM.DIST(75,78,1.1679943,TRUE) The average amount of water in randomly selected 16-ounce bottles of water is 15.9 ounces with a standard deviation of 0.6 ounces. If a random sample of sixty-four 16- ounce bottles of water are selected, what is the probability that the mean of this sample is less than 15.7 ounces of water? Answer: (round to 4 decimal places) New SD = .6/SQRT(64) P(x < 15.7), in Excel =NORM.DIST(15.7,15.9,0.075,TRUE) The average amount of a beverage in randomly selected 16-ounce beverage can is 16 ounces with a standard deviation of 0.4 ounces. If a random sample of sixty-four 16- ounce beverage cans are selected, what is the probability that the mean of this sample is less than 16.1 ounces of beverage? Answer: (round to 4 decimal places) New SD = .4/SQRT(64) P(x < 16.1), in Excel =NORM.DIST(16.1,16,0.05,TRUE) The final exam grade of a statistics class has a skewed distribution with mean of 78 and standard deviation of 7.8. If a random sample of 36 students selected from this class,

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12/30/23, 12:36 AM - MATH302 D002 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/148218?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequence… 10/10 ___ 0.9275___ Hide ques±on 20 feedback Done then what is the probability that the average final exam grade of this sample is between 75 and 80? Answer: (round to 4 decimal places) New SD = 7.8/SQRT(36) P( 75 < x < 80), in Excel =NORM.DIST(80,78,1.3,TRUE)-NORM.DIST(75,78,1.3,TRUE)

Week 4 Knowledge Check Homework Practice Questions

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