Download Ch 3 Worked Problems - University of Arizona Math

6. (3.14) The total scores on the Medical College Admission Test (MCAT) follow a Normal
distribution with mean 24.7 and standard deviation 6.5.
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What are the median and the first and third qdartiles of the MCAT scores? Median=Mean
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9. (3.20) According to a study, the scale of scores on an IQ test of adults is approximately
Normal with mean 104 and standard deviation 13 . The organization MENSA, which calls
itself "the high-IQ society," requires an IQ score of 130 or higher for membership.
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What percent of adults(± 0.1 %) would qualify for membership? 2.3%
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(3.22) The proportion of observations from a standard Normal distribution that take values
greater than 1.73 is out (±0.001) Q.041 8
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less than -1.29 s about (±0.0001) 0.0985
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12. (3.29) (a) Use your calculator to find the numbe@-~~lS v CA.. \u-e_
such that the proporti~servations that are less thanz in a standard Normal distribution is
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13. (3 .3 3) Automated manufacturing operations are quite J>recise but still ~ry, often with
distributions that are close to Normal. The width in inches of slots cut by a milling machine
follows approximately the N(0.8750,0.0013) distribution. The specifications allow slot widths
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between 0.8725 and 0.8775 inch. ~
What proportion (±0.001) of slots meet these specifications (use software)'(Oj450
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14. (3.37) NOTE: The numerical values in this problem have been modified for testing
purposes. In its Fuel Economy Guide for 2014 model vehicles, the Environmental
Protection Agency gives data on 1160 vehicles. There are a number of high outliers, mainly
hybrid gas-electric vehicles. If we ignore the vehicles identified as outliers, however, the
combined city and highway gas mileage of the other 1134 vehicles is approximately Normal
with mean 22.6 miles per gallon (mpg) and standard-deviation .2_2 mpg. The quartiles of any
distribution are1lie values with cumulative proportions 0.25 and 0.75. They span the middle
half of the distribution. What are the quartiles (±0.01) of the distribution of gas mileage?
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The first quartile is 19.09 mpg.
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The third quartile is 26.11mpg. (
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ts on an IQ test are approximately Normal with mean 100 and
standard deviation 15. Clara s.cores .142 on such a test. She scores higher than what Eerc~t
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She scores higher than 99.74% o/an ad}lfts.
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17. (3.28) Find the proportion of observations (±0.0001) from a standard Normal distribution
that falls in each of the following regions. In each sketch a standard Normal curve and shade )
the area representing the region.
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18. (3.32) In a study of exercise, a large group of male runners walk on a treadmill foro
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minutes. Their heart rates in beats per minute at the end vary from runner to runner
according to
N(103, 13) distribution. The heart rates for male nonrunners after the same
ave the M 131 , 17.3 ) distribution.
(a) What
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cent (±.1) of the runners have heart rates above 135 (use software)? 0.69%
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at percent (±0.1) of the n2,nrunners.have heart rates above 135 (use software)? 40.86%
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19. (3.36) NOTE: The numerical values in this problem have been modified for testing purposes.
In its Fuel Economy Guide for 2014 model vehicles, the Environmental Protection Agency gives
data on 1160 vehicles. There are a number of high outliers, mainly hybrid gas-electric vehicles.
If we ignore the vehicles identified as outliers, however, the combined city and highway gas
mileage of the other 1134 vehicles is approximately Normal with mean 23 miles per gallon
(mpg) and standard deviation 5.2 mpg. How high must a 2014 vehicle's gas mileage (±0.01) be
to fall in the top 10% of all vehicles?
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(3.38) NOTE: The numerical talues in this problem have been modified for testing
purposes.
Gas mileage= 29.66mpg
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In its Fuel Economy Guide for 2014 model vehicles, the Environmental Protection Agency
gives data on 1160 vehicles. There are a number of high outliers, mainly hybrid gaselectric vehicles. If we ignore the vehicles identified as outliers, however, the combined
city and highway gas mileage of the other 1134 vehicles is approximately Normal with
mean 22.9 miles per gallon (mpg) and standard deviation 5.2 mpg.
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The quintiles of any distribution are the values with cumulative proportions 0.20, 0.40,
0.60, and 0.80. What are the quintiles of the distribution of gas mileage?
The first quinti1e is (±0.01 mpg) 18.5237 mpg.
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The second quinti1e is (±0.01 mpg) 21.5828mpg.
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The third quinti1e is (±0.01 mpg) 24.2172mpg. \
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The fourth quinti1e is (±0.01 mpg) 27.2763mpg.
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