Week 4 Test

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American Public University *

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302

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Statistics

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Feb 20, 2024

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11

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Week 4 Test - Results X Attempt 1 of 2 Written Sep 25, 2023 11:55 AM - Sep 25, 2023 1:26 PM Attempt Score 18 /20 -90 % Overall Grade (Highest Attempt) 20 /20 - 100 % Question 1 1/ 1 point Find the area under the standard normal distribution to the left of z = -1.35. Round answer to 4 decimal places. Answer: 0.0885 v w Hide question 1 feedback In Excel, =NORM.S.DIST(-1.35,TRUE) Question 2 1/ 1 point A dishwasher has a mean life of 11.5 years with an estimated standard deviation of 1.5 years ("Appliance life expectancy,' 2013). Assume the life of a dishwasher is normally distributed. Find the number of years that the bottom 10% of dishwasher would last. Round answer to 2 decimal places. Answer: 958 v ¥ Hide question 2 feedback In Excel, =NORM.INV(0.1,11.5,1.5)
Question 3 1/ 1 point 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 47.8 cm and a standard deviation of 3.72 cm (Ovegard, Berndt & Lunneryd, 2012). Assume the length of fish is normally distributed. What is the length in cm of the longest 10% of Atlantic cod in this area? Round answer to 2 decimal places. Answer: 52.57 v w Hide question 3 feedback Longest 10% is in the 90th percentile. In Excel, =NORM.INV(.90,47.8,3.72) Question 4 1/ 1 point Which type of distribution does the graph illustrate? > Poisson Distribution ¢<> Right skewed Distribution ) Uniform Distribution ) Normal Distribution 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 27.4 mpg and a standard deviation of 10.2 mpg. If 29 such cars are tested, what is the probability the average mpg achieved by these 29 cars will be greater than 29? Answer: ___ Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate entry. Make sure you include the O before the decimal. Answer: 0.1991 v w Hide question 5 feedback This is a sampling distribution problem with u=27.4. 0 = 10.2, and sample sizen = 29. New SD = 10.2/SQRT(29) = 1.894092 P(x > 29) =1 - NORM.DIST(29, 27.4,1.894092, TRUE) Question 6 1/ 1 point The average lifetime of a certain new cell phone is 4.2 years. The manufacturer will replace any cell phone failing within three years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution. The decay rate is: v 02381 07619 ~0.3333 ) 0.6667
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¥ Hide question 6 feedback 1/4.2 Question 7 1/ 1 point The average lifetime of a set of tires is 3.4 years. The manufacturer will replace any set of tires failing within three 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 three years of the date of purchase? v() 0.5862 04138 () 0.4866 - 0.7568 w Hide question 7 feedback P(x < 3) In Excel, =EXPON.DIST(3,1/3.4,TRUE) Question 8 1/ 1 point Suppose that the longevity of a light bulb is exponential with a mean lifetime of 7.6 years. Find the probability that a light bulb lasts less than three years. \/(j) 0.3261
) 8.5634 ) 0.6739 ~0.3907 w Hide question 8 feedback P(x < 3) In Excel, =EXPON.DIST(3,1/7.6,TRUE) Question 9 1/ 1 point The life of an electric component has an exponential distribution with a mean of 8.9 years. What is the probability that a randomly selected one such component has a life more than 8 years? Answer: (Round to 4 decimal places.) 0.4070 v ¥ Hide question 9 feedback P(x > 8) 1-P(x < 8) =1-EXPON.DIST(8,1/8.9,TRUE) Question 10 1/ 1 point Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The probability that a random vehicle gets between 25 and 30 miles per gallon is: Answer: (Round to four decimal places) 0.2083 v
w Hide question 10 feedback Interval goes from 23 < x < 47 P(25 <x <30)=(30-25)* 47 23 Question 11 1/ 1 point The waiting time for a bus has a uniform distribution between 2 and 11 minutes. What is the 75th percentile of this distribution? . minutes Answer: (Round answer to two decimal places.) 875 v w Hide question 11 feedback P(X < x)=.75 75 = T 2 11 2 75*9 =x-2 6.75+2=x 8.75 =x Question 12 1/ 1 point
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Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The probability that a random vehicle gets between 28 and 36 miles per gallon is: Answer: (Round to four decimal places) ___0.3333 __ v w Hide question 12 feedback Interval goes from 23 < x < 47 P(28 < x < 36) = (36 - 28)* 47 23 Question 13 1/ 1 point Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The probability that a random vehicle gets between 25 and 34 miles per gallon is: Answer: (Round to three decimal places) ___ 0.375 v W Hide question 13 feedback Interval goes from 23 < x < 47 P(25 <x<34)=(34-25)" 47 23 Question 14 1/ 1 point
A local grocery delivery time has a uniform distribution over 15 to 65 minutes. What is the probability that the grocery delivery time is more than 20 minutes on a given day? Answer: (Round to 2 decimal places.) 090 v w Hide question 14 feedback Interval goes from 15 < x < 65 P(x > 20) = (65 - 20) * 65 15 Question 15 1/ 1 point Miles per gallon of a vehicle is a random variable with a uniform distribution from 22 to 39. The probability that a random vehicle gets between 26 and 31 miles per gallon is: Answer: (Round to four decimal places) ___0.2941 v w Hide question 15 feedback Interval goes from 22 < x<39 1 39 22 P(26 < z < 31) = (31 26) = Question 16 0/ 1 point The average amount of a beverage in randomly selected 16-ounce beverage can is 16.18 ounces with a standard deviation of 0.38 ounces. If a random sample of eighty 16-ounce beverage cans are selected, what is the probability
that mean of this sample is less than 16.1 ounces of beverage? Answer: (round to 4 decimal places) 0.0301 % (0.0298,.0298) ¥ Hide question 16 feedback New SD = .38/SQRT(80) = 0.042485 P(x < 16.1), in Excel =NORM.DIST(16.1,16.18,0.042485,TRUE) Question 17 1/ 1 point The average amount of a beverage in randomly selected 16-ounce beverage can is 15.96 ounces with a standard deviation of 0.5 ounces. If a random sample of sixty-five 16-ounce beverage cans are selected, what is the probability that the mean of this sample is less than 16.05 ounces of beverage? Answer: (round to 4 decimal places) 0.9266 v w Hide question 17 feedback New SD =.5/SQRT(65) = 0.062017 P(x < 16.05), in Excel =NORM.DIST(16.05,15.96,0.062017,TRUE) Question 18 1/ 1 point The average credit card debt for college seniors is $22,199 with a standard deviation of $5300. What is the probability that a sample of 30 seniors owes a mean of more than $20,200? Round answer to 4 decimal places. Answer: 0.9806 v ¥ Hide question 18 feedback
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New SD = 5300/SQRT(30) = 967.6432 P(x > 20200), using Excel =1-NORM.DIST(20200,22199,967.6432,TRUE) Question 19 0/ 1 point The final exam grade of a statistics class has a skewed distribution with mean of 79.8 and standard deviation of 8.2. If a random sample of 45 students selected from this class, then what is the probability that the average final exam grade of this sample is between 80 and 83? Answer: (round to 4 decimal places) ___0.4320 % (0.4306, .4306) w Hide question 19 feedback New SD = 8.2/SQRT(45) = 1.222384 P(80 < x < 83), in Excel =NORM.DIST(83,79.8,1.222384,TRUE)- NORM.DIST(80,79.8,1.222384,TRUE) Question 20 1/ 1 point The final exam grade of a mathematics class has a normal distribution with mean of 81 and standard deviation of 6.6. If a random sample of 40 students selected from this class, then what is the probability that the average final exam grade of this sample is between 77 and 82? Answer: (round to 4 decimal places) __ 0.8310 v w Hide question 20 feedback New SD = 6.6/SQRT(40) = 1.043552 P(77 < x < 82), in Excel
=NORM.DIST(82,81,1.043552,TRUE)-NORM.DIST(77,81,1.043552,TRUE) Done