STATS WK IV HOMEWORK

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Garden City Community College *

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302

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Statistics

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Jan 9, 2024

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Question 1 0 / 1 point Find P(Z ≤ 3). Round answer to 4 decimal places. Answer: ___.0013 ___ (0.9987, .9987) Hide question 1 feedback In Excel, =NORM.S.DIST(3,TRUE) Question 2 1 / 1 point Find P(-1.96 ≤ Z ≤ 1.96). Round answer to 2 decimal places. Answer: ___.95 ___ Hide question 2 feedback In Excel, =NORM.S.DIST(1.96,TRUE)-NORM.S.DIST(-1.96,TRUE) Question 3 1 / 1 point Find P(1.31 < Z < 2.15). Round answer to 4 decimal places. Answer: ___.0793 ___ Hide question 3 feedback In Excel, =NORM.S.DIST(2.15,TRUE)-NORM.S.DIST(1.31,TRUE) Question 4 1 / 1 point Which type of distribution does the graph illustrate? Uniform Distribution Poisson Distribution Normal Distribution Right skewed Distribution Question 5 The cost of unleaded gasoline in the Bay Area once followed a normal distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations

from the Bay area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. What is the approximate probability that the average price for 16 gas stations is over $4.69? 0.1587 Almost zero Unknown 0.0943 Hide question 5 feedback New SD = .10/SQRT(16) = .025 P(x > 4.69) = 1 - P(x < 4.69) In Excel, =1-NORM.DIST(4.69,4.59,.025,TRUE) You might get an answer with an "E" in it. The "E"; means scientific notation. 3.16712E-05 decimal answer is, .0000316712 Question 6 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? 0.8647 0.2212 0.4866 0.9997 Hide question 6 feedback P(x < 2) In Excel, =EXPON.DIST(2,1/3,TRUE) Question 7 1 / 1 point 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) ___.314 ___ Hide question 7 feedback 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) Question 8 1 / 1 point The life of an electric component has an exponential distribution with a mean of 8 years. What is the probability that a randomly selected one such component has a life less than 5 years? Answer: (round to 4 decimal places) ___.4647 ___ Hide question 8 feedback P(x < 5) In Excel, =EXPON.DIST(5,1/8,TRUE) Question 9 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. What is the median lifetime of these phones (in years)? 5.5452 1.3863 0.1941 2.0794 Hide question 9 feedback Median Lifetime is the 50th percentile. Use .50 in the equation and the rate of decay is 1/3 Question 10 1 / 1 point The waiting time for a table at a busy restaurant has a uniform distribution between 0 and 10 minutes. What is the 95th percentile of this distribution? (Recall: The 95th percentile divides the distribution into 2 parts so that 95% of area is to the left of 95th percentile) _______ minutes Answer: (Round answer to one decimal place.)

___9.5 ___ Hide question 10 feedback Interval goes from 0 < x < 10. 95th percentile use .95 P(X < x) = .95 .95*10 = x 9.5 = x Question 11 1 / 1 point 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) ___.50 ___ Hide question 11 feedback Interval goes from 25 < x < 35 P(25 < x < 30) = Question 12 1 / 1 point A local pizza restaurant delivery time has a uniform distribution over 0 to 60 minutes. What is the probability that the pizza delivery time is more than 25 minutes on a given day? Answer: (Round to 2 decimal places.) ___.58 ___ Hide question 12 feedback Interval goes from 0 < x < 60 P(x > 25) = Question 13 1 / 1 point The waiting time for a taxi has a uniform distribution between 0 and 10 minutes. What is the probability that the waiting time for this taxi is less than 7 minutes on a given day? Answer: (Round to two decimal place.) ___.70 ___ Hide question 13 feedback Interval goes from 0 < x < 10 P(x < 7) = Question 14 1 / 1 point 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.) ___.60 ___ Hide question 14 feedback Interval goes from 0 < x < 10 P(x > 4) = Question 15 1 / 1 point 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 6 minutes on a given day? Answer: (Round to two decimal place.) ___.60 ___ Hide question 15 feedback Interval goes from 0 x 10 P(x < 6) = Question 16 1 / 1 point

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The average amount of a beverage in randomly selected 16-ounce beverage can is 15.8 ounces with a standard deviation of 0.5 ounces. If a random sample of thirty-six 16-ounce beverage cans are selected, what is the probability that the mean of this sample is less than 15.7 ounces of beverage? Answer: (round ___.1151 ___ Hide question 16 feedback New SD =.5/SQRT(36) P(x <15.7), in Excel =NORM.DIST(15.7,15.8,0.08333,TRUE) Question 17 1 / 1 point 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) ___.9515 ___ Hide question 17 feedback 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) Question 18 0 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) ___.0260 ___ (0.0038, .0038) Hide question 18 feedback New SD = .6/SQRT(64) P(x < 15.7), in Excel =NORM.DIST(15.7,15.9,0.075,TRUE) Question 19 1 / 1 point A certain brand of electric bulbs has an average life of 300 hours with a standard deviation of 45. A random sample of 100 bulbs is tested. What is the probability that the sample mean will be less than 295? 0.3667 0.4558 -1.1111 0.1333 Hide question 19 feedback New SD = 45/SQRT(10) P(x < 295), in Excel =NORM.DIST(295,300,4.5,TRUE) New SD = 45/SQRT(10) P(x < 295), in Excel =NORM.DIST(295,300,4.5,TRUE) Question 20 1 / 1 point The final exam grade of a statistics class has a skewed distribution with mean of 76 and standard deviation of 7.6. If a random sample of 32 students selected from this class, then what is the probability that average final exam grade of this sample is between 75 and 80? Answer: (round to 4 decimal places) ___.7702 ___ Hide question 20 feedback New SD = 7.6/SQRT(32) P(75 < x < 80), in Excel =NORM.DIST(80,76,1.3435,TRUE)-NORM.DIST(75,76,1.3435,TRUE)

STATS WK IV HOMEWORK

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