statistics problems
Statistics 10 questions
|
Girls x |
P(x) |
|
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|
0 |
0.0040.004 |
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|
1 |
0.0210.021 |
|||||||||||||
|
2 |
0.1060.106 |
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|
3 |
0.2040.204 |
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|
4 |
0.3300.330 |
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|
5 |
0.2040.204 |
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|
6 |
0.1060.106 |
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|
7 |
0.0210.021 |
|||||||||||||
|
8 |
0.0040.004 |
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The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below.
Click the icon to view the table.
a. Find the probability of getting exactly 1 girl in 8 births.
nothing
(Type an integer or a decimal. Do not round.)
b. Find the probability of getting 1 or fewer girls in 8 births.
nothing
(Type an integer or a decimal. Do not round.)
c. Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part (a) or part (b)?
A.
Since the probability of getting 0 girls is less likely than getting 1 girl, the result from part (a) is the relevant probability.
B.
Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability.
C.
Since the probability of getting 1 girl is the result from part (a), this is the relevant probability.
D.
Since getting 0 girls is an even lower number of girls than getting 1 girl, the result from part (b) is the relevant probability.
d. Is 1 a significantly low number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event.
A.
No, since the appropriate probability is greater than 0.05, it is not a significantly low number.
B.
No, since the appropriate probability is less than 0.05, it is not a significantly low number.
C.
Yes, since the appropriate probability is greater than 0.05, it is a significantly low number.
D.
Yes, since the appropriate probability is less than 0.05, it is a significantly low number.
2. Assume that random guesses are made for 66 multiple-choice questions on a test with
55 choices for each question, so that there are n equals=66 trials, each with probability of success (correct) given by p equals=0.200.20. Find the probability of no correct answers.
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The probability of no correct answers is
nothing .
(Round to three decimal places as needed.)
3. A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 4747 tablets, then accept the whole batch if there is only one or none that doesn’t meet the required specifications. If one shipment of 30003000 aspirin tablets actually has a 33% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is
nothing .(Round to four decimal places as needed.), The company will acceptsnothing %
of the shipments and will reject
nothing %
of the shipments, so
(Round to two decimal places as needed.)
4. For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are
a. significantly high (or at least 2 standard deviations above the mean).
b. significantly low (or at least 2 standard deviations below the mean).
c. not significant (or less than 2 standard deviations away from the mean).
a. The percentage of bone density scores that are significantly high is
nothing %.
(Round to two decimal places as needed.)
b. The percentage of bone density scores that are significantly low is
nothing %.
(Round to two decimal places as needed.)
c. The percentage of bone density scores that are not significant is
nothing %.
(Round to two decimal places as needed.)
5. Assume that an adult female is randomly selected. Suppose females have pulse rates that are normally distributed with a mean of 74.074.0 beats per minute and a standard deviation of 12.512.5 beats per minute. Find the probability of a pulse rate between 6060 beats per minute and 7070 beats per minute. (Hint: Draw a graph.)
The probability is nothing .(Round to four decimal places as needed.)
6. An airliner carries 150150 passengers and has doors with a height of 7575 in. Heights of men are normally distributed with a mean of 69.069.0 in and a standard deviation of 2.82.8 in. Complete parts (a) through (d).
a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
The probability is (Round to four decimal places as needed.)
b. If half of the 150150 passengers are men, find the probability that the mean height of the 7575 men is less than 7575 in.
The probability is (Round to four decimal places as needed.)
c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?
A.
The probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend.
B.
The probability from part (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.
C.
The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.
D.
The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.
d. When considering the comfort and safety of passengers, why are women ignored in this case?
A.
There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.
B.
Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.
C.
Since men are generally taller than women, it is more difficult for them to bend when entering the aircraft. Therefore, it is more important that men not have to bend than it is important that women not have to bend.
7.Aclinical trial tests a method designed to increase the probability of conceiving a girl. In the study 664664 babies were born, and 332332 of them were girls. Use the sample data to construct a 9999%
confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?
nothing less than< p less than<nothing
(Round to three decimal places as needed.)
Does the method appear to be effective?
No,the proportion of girls is notis not significantly different from 0.5.
Yes, the proportion of girls is significantly different from 0.5.
8. In the week before and the week after a holiday, there were
10 comma 00010,000
total deaths, and
49404940
of them occurred in the week before the holiday.
a. Construct a
9090%
confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday.
b. Based on the result, does there appear to be any indication that people can temporarily postpone their death to survive the holiday?
a.
nothing less than<pless than<nothing
(Round to three decimal places as needed.)
b. Based on the result, does there appear to be any indication that people can temporarily postpone their death to survive the holiday?
YesYes,
because the proportion
could notcould not
easily equal 0.5. The interval
isis
substantially less than 0.5 the week before the holiday.
NoNo,
because the proportion
couldcould
easily equal 0.5. The interval
is notis not
less than 0.5 the week before the holiday.
9. A data set includes
103103
body temperatures of healthy adult humans having a mean of
98.398.3degrees°F
and a standard deviation of
0.730.73degrees°F.
Construct a
9999%
confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of
98.6degrees°F
as the mean body temperature?
Click here to view a t distribution table.
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Click here to view page 1 of the standard normal distribution table.
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Click here to view page 2 of the standard normal distribution table.
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What is the confidence interval estimate of the population mean
muμ?
nothing degrees°Fless than<muμless than<nothing degrees°F
(Round to three decimal places as needed.)
What does this suggest about the use of
98.6degrees°F
as the mean body temperature?
A.
This suggests that the mean body temperature could
be lower thanbe lower than
98.6degrees°F.
B.
This suggests that the mean body temperature could
very possibly bevery possibly be
98.6degrees°F.
C.
This suggests that the mean body temperature could
be higher thanbe higher than
98.6degrees°F.
10. accompanying data set and construct a 9090% confidence interval estimate of the mean pulse rate of adult females; then do the same for adult males. Compare the results.
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Click the icon to view the pulse rates for adult females and adult males.
Construct a
9090%
confidence interval of the mean pulse rate for adult females.
nothing
bpmless than<muμless than<nothing
bpm
(Round to one decimal place as needed.)
Construct a
9090%
confidence interval of the mean pulse rate for adult males.
nothing
bpmless than<muμless than<nothing
bpm
(Round to one decimal place as needed.)
Compare the results.
A.
The confidence intervals do not overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.
B.
The confidence intervals overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.
C.
The confidence intervals do not overlap, so it appears that adult females have a significantly higher mean pulse rate than adult males.
D.
The confidence intervals overlap, so it appears that adult males have a significantly higher mean pulse rate than adult females.
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