Download Math 116 - Chapters 3-5

Math 116 - Chapters 3-5
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Problems are all mixed up. The three chapters require finding probabilities with very different procedures.
Write a two-page study guide outlining the methods/formulas of the three chapters.
Show all your work on another paper.
Remember to sketch graphs whenever needed.
Problems from chapter 4 and 5 should be solved by hand and with a feature in the calculator.
Indicate the feature used and how you entered in the calculator.
The spring break is meant to catch up, not to waste one whole week doing nothing. Please, study! Your grade on the next
exam depends on this.
THINK ABOUT THE FOLLOWING:
IT'S ONLY 8 MORE WEEKS TO FINISH THE SEMESTER AND PASS THE CLASS, OR........ 8 MORE WEEKS AND
ANOTHER SEMESTER.
Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard
deviations. That is, unusual values are either less than m - 2s or greater than m + 2s.
1) According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to
"Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are
randomly selected and checked to determine what is being watched. Would it be unusual to find that 899 of the
2500 televisions are tuned to "Eyewitness News"?
Solve the problem.
2) In a certain town, 20% of adults have a college degree. The accompanying table describes the probability
distribution for the number of adults (among 4 randomly selected adults) who have a college degree.
a) Show how you find each one of those probabilities. Also check the answers with a feature of the calculator.
Specify instructions entered in calculator.
x
P(x)
0 0.4096
1 0.4096
2 0.1536
3 0.0256
4 0.0016
b) Use the probability rule to identify unusual scores. Must explain or show work.
3) For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and
a standard deviation of 13.1. If 23 women aged 18-24 are randomly selected, find the probability that their
mean systolic blood pressure is between 119 and 122.
4) Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard
deviation of 2.5 inches. Find the value of the quartile Q3 .
5) The grades on the final exam for all students who took Math 160 in a certain semester are normally distributed
with a mean of 73 and a standard deviation 7.8. If 24 students are randomly selected, find the probability that
the mean of their test scores is greater than 78.
6) The scores on a certain test are normally distributed with a mean score of 45 and a standard deviation of 3.
What is the probability that a sample of 90 students will have a mean score of at least 45.3162?
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7) The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 140 mm Hg
and a standard deviation of 13.2 mm Hg. Find the two blood pressures having these properties: the mean is
midway between them and 90% of all blood pressures are between them.
Answer the question.
8) Focus groups of 15 people are randomly selected to discuss products of the Famous Company. It is determined
that the mean number (per group) who recognize the Famous brand name is 10.2, and the standard deviation is
0.87. Would it be unusual to randomly select 15 people and find that greater than 14 recognize the Famous
brand name?
Find the indicated probability.
9) Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation
0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of
legal quarters will be rejected?
10) A car insurance company has determined that 7% of all drivers were involved in a car accident last year.
Among the 14 drivers living on one particular street, 3 were involved in a car accident last year. If 14 drivers are
randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?
11) The probability that Luis will pass his statistics test is 0.74. Find the probability that he will fail his statistics
test.
12) In a poll, respondents were asked whether they had ever been in a car accident. 127 respondents indicated that
they had been in a car accident and 299 respondents said that they had not been in a car accident. If one of
these respondents is randomly selected, what is the probability of getting someone who has been in a car
accident? Round to the nearest thousandth, if necessary.
13) An airline estimates that 90% of people booked on their flights actually show up. If the airline books 65 people
on a flight for which the maximum number is 63, what is the probability that the number of people who show
up will exceed the capacity of the plane?
14) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
a) If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and drinks cola.
b) If one person is randomly selected, find the probability that the person drinks root beer or lemon-lime?
c) If one person is randomly selected, find the probability that the person drinks root beer or is between 21 and
40?
15) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a
standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between
200 and 275.
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Find the mean and the standard deviation of the given probability distribution.
16) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970,
0.1307, 0.0191, and 0.0010, respectively. Round answer to the nearest hundredth.
ALSO, DETERMINE USUAL AND UNUSUAL VALUES BY USING
A) THE PROBABILTIY RULE
B) THE RANGE RULE OF THUMB
Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread
evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of
pounds lost.
17) Between 6 pounds and 9 pounds
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0e C at
the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water,
some give readings below 0e C (denoted by negative numbers) and some give readings above 0e C (denoted by positive
numbers). Assume that the mean reading is 0e C and the standard deviation of the readings is 1.00e C.Also assume that the
frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and
tested. Find the temperature reading corresponding to the given information.
18) If 6.3% of the thermometers are rejected because they have readings that are too high and another 6.3% are
rejected because they have readings that are too low, find the two readings that are cutoff values separating the
rejected thermometers from the others.
Using the following uniform density curve, answer the question given on problem 19.
19) What is the probability that the random variable has a value less than 4.1?
Find the indicated probability.
20) In a certain college, 30% of the physics majors belong to ethnic minorities. If 10 students are selected at random
from the physics majors,
a) What is the probability that no more than 6 belong to an ethnic minority?
b) What is the probability that at least 3 belong to an ethnic minority?
c) What is the probability that between 4 and 7 inclusive belong to an ethnic minority.
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Answer Key
Testname: PRACTICECH3-5
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
No
3 and 4
0.0577
65.3 inches
0.0008
0.1587
118.3 mm Hg, 161.7 mm Hg
Yes
1.96%
0.0698
0.26
0.298
0.0087
4
32
28
14) a)
, b)
, c)
51
51
51
15) 0.4332
16) 0.72, 0.77
1
17)
2
18) -1.53e , 1.53e
19) 0.5125
20) a) 0.9894, b) .6172, c) .3488
4