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# MATH 221 Statistics WEEK 8 PROBLEMS

Subject: Mathematics / Statistics Question•The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester.

?(a) Find the probability that a randomly selected student is? male, given that the student is a nursing major.
?(b) Find the probability that a randomly selected student is a nursing? major, given that the student is male.
Nursing Majors
?Non-nursing majors
Total
Males
93
1102
1195
Females
725
1691
2416
Total
818
2793
3611
?(a) Find the probability that a randomly selected student is? male, given that the student is a nursing major.
The probability is
.
?(Round to three decimal places as? needed.)
?
(b) Find the probability that a randomly selected student is a nursing? major, given that the student is male.
The probability is
.
?(Round to three decimal places as? needed.)

•The probability that a person in the United States has type B?+blood is 99?%. Three unrelated people in the United States are selected at random. Complete parts? (a) through? (d).
?(a) Find the probability that all three have type B?+blood.
The probability that all three have type B?+blood is
.
?(Round to six decimal places as? needed.)
?
(b) Find the probability that none of the three have type B?+blood.
The probability that none of the three have type B?+blood is
.
?(Round to three decimal places as? needed.)
?
(c) Find the probability that at least one of the three has type B?+blood.
The probability that at least one of the three has type B?+blood is
.
?(Round to three decimal places as? needed.)
(d) Which of the events can be considered? unusual? Explain. Select all that apply.
A.The event in part? (b) is unusual because its probability is less than or equal to 0.05.
B.None of these events are unusualNone of these events are unusual.
C.The event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05The event in part (a) is unusual because its probability is less than or equal to 0.05.
D.The event in part? (c) is unusual because its probability is less than or equal to 0.05.
•The table below shows the results of a survey that asked 2869 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts? (a) through? (e).
Frequently???
Occasionally
Not at all
Total
Male
228228
459
797
1484
Female
203203
440
742
1385
Total
431431
899
1539
2869
?
(a) Find the probability that the person is frequently or occasionally involved in charity work.
P(being frequently involved or being occasionally involved)=
?(Round to the nearest thousandth as? needed.)
?(b) Find the probability that the person is female or not involved in charity work at all.
P(being female or not being involved)=
?(Round to the nearest thousandth as? needed.)
?
(c) Find the probability that the person is male or frequently involved in charity work.
P(being male or being frequently involved)=
?(Round to the nearest thousandth as? needed.)
?
(d) Find the probability that the person is female or not frequently involved in charity work.
P(being female or not being frequently involved)=
?(Round to the nearest thousandth as? needed.)
?
(e) Are the events? “being female” and? “being frequently involved in charity? work” mutually? exclusive? Explain.
A.?No, because 203 females are frequently involved in charity work.
B.?Yes, because 203 females are frequently involved in charity work.
C.?No, because no females are frequently involved in charity work.
D.?Yes, because no females are frequently involved in charity work.

•Evaluate the given expression and express the result using the usual format for writing numbers? (instead of scientific? notation).
47P2
47P2=
•Outside a? home, there is a 4?-key keypad with letters A, B, C, and D that can be used to open the garage if the correct four?-letter code is entered. Each key may be used only once. How many codes are? possible?
The number of possible codes is .

•Use the normal distribution of fish lengths for which the mean is 9 inches and the standard deviation is 5 inches. Assume the variable x is normally distributed.
(a) What percent of the fish are longer than 12 inches?
(b) If 500 fish are randomly selected, how many would you expect to be shorter than 8 inches?
(a) Approximately ?% of fish are longer than 12 inches.
?(Round to two decimal places as? needed.)
(b) You would expect approximately fish to be shorter than 8 inches.
?(Round to the nearest? fish.)??

•The time spent? (in days) waiting for a heart transplant for people ages? 35-49 can be approximated by the normal? distribution, as shown in the figure to the right..0/msohtmlclip1/01/clip_image001.jpg”>
?(a) What waiting time represents the 55th ?percentile?
?(b) What waiting time represents the third? quartile?

?(a) The waiting time that represents the 55th percentile isdays.
?(Round to the nearest integer as? needed.)
?(b) The waiting time that represents the third quartile isdays.
?(Round to the nearest integer as? needed.)
•A machine cuts plastic into sheets that are 35 feet ?(420 ?inches) long. Assume that the population of lengths is normally distributed. Complete parts? (a) and? (b).
?(a)
The company wants to estimate the mean length the machine is cutting the plastic within
0.125 inch. Determine the minimum sample size required to construct a 90?%
confidence interval for the population mean. Assume the population standard deviation is 0.25
inch.
n=
?(Round up to the nearest whole number as? needed.)
?(b)
Repeat part? (a) using an error tolerance of 0.0625 inch.
n=
?(Round up to the nearest whole number as? needed.)
Which error tolerance requires a larger sample? size? Explain.
A.The tolerance =0.125 inch requires a larger sample size. As error size? increases, a larger sample must be taken to ensure the desired accuracy.
B.The tolerance =0.0625 inch requires a larger sample size. As error size? increases, a larger sample must be taken to ensure the desired accuracy.
C.The tolerance =0.125 inch requires a larger sample size. As error size? decreases, a larger sample must be taken to ensure the desired accuracy.
D.The tolerance =0.0625 inch requires a larger sample size. As error size? decreases, a larger sample must be taken to ensure the desired accuracy.
•Construct the indicated confidence interval for the population mean? using a? t-distribution.
c=0.99?, x overbar=105?, s=10?, n=27
The confidence interval is (,.)
?(Round to the nearest tenth as? needed.)
•In a survey of 2349 ?adults, 738 say they believe in UFOs. Construct a 99% confidence interval for the population proportion of adults who believe in UFOs.
A 99?% confidence interval for the population proportion is
?( ?, ?).
?(Round to three decimal places as? needed.)
A. With 99?% ?confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
B.The endpoints of the given confidence interval shows that 99?% of adults believe in UFOs.
C.With 99?% ?confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
D.With 99?% ?probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.
•A researcher wishes to? estimate, with 95?% ?confidence, the population proportion of adults who are confident with their? country’s banking system. His estimate must be accurate within 55?% of the population proportion.
?(a) No preliminary estimate is available. Find the minimum sample size needed.
?(b) Find the minimum sample size? needed, using a prior study that found that 34?% of the respondents said they are confident with their? country’s banking system.
(c) ?Compare the results from parts ?(a) and ?(b).

?(a) What is the minimum sample size needed assuming that no prior information is? available?
n=
?(Round up to the nearest whole number as? needed.)
?
(?b) What is the minimum sample size needed using a prior study that found that 34?% of the respondents said they are confident with their? country’s banking? system?
n=
?(Round up to the nearest whole number as? needed.)
?(c) How do the results from ?(a) and ?(b)? compare?
A. Having an estimate of the population proportion has no effect on the minimum sample size needed.
B.Having an estimate of the population proportion raises the minimum sample size needed.
C.Having an estimate of the population proportion reduces the minimum sample size needed.
•Use a? t-test to test the claim about the population mean? at the given level of significance? using the given sample statistics. Assume the population is normally distributed.
?Claim:??24?;?=0.10
Sample? statistics: x overbar=27.1?, s=4.9?, n=13
What are the null and alternative? hypotheses? Choose the correct answer below.
A.H0?:?=24
Ha?:??24
B.H0?:??24
Ha?:?>24
C.H0?:??24
Ha?:?=24
D.H0?:??24
Ha?:?<24
What is the value of the standardized test? statistic?
The standardized test statistic is
.
?(Round to two decimal places as? needed.)
What is the? P-value of the test? statistic?
?P-=
?(Round to three decimal places as? needed.)
Decide whether to reject or fail to reject the null hypothesis.
A. Fail to reject H0. There is enough evidence to support the claim.
B.Reject H0. There is not enough evidence to support the claim.
C.Fail to reject H0. There is not enough evidence to support the claim.
D.Reject H0. There is enough evidence to support the claim.
•One? study, based on responses from 1,025 randomly selected? teenagers, concluded that 43?% of teenagers cite grades as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of all teenagers in the population feel that grades are their greatest source of pressure.
Formulate the null and alternative hypotheses. Choose the correct answer below.
A. H0?: p=0.5
Ha?: p?0.5
B.H0?: p=0.5
Ha?: pr than>0.5
C.H0?: p<0.5
Ha?: =0.5
D.H0?: p=0.5
Ha?: p<0.5
Find the test statistic.
z=
?(Round to two decimal places as? needed.)
Find the? P-value for the found test statistic.
?P-value=
?(Round to four decimal places as? needed.)
State the conclusion. Choose the correct answer below.
A. Do not reject H0. There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
B.Do not reject H0. There is insufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
C.Reject H0. There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
D.Reject H0. There is insufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
•The equation used to predict the total body weight? (in pounds) of a female athlete at a certain school is y=?117 + 3.57×1+ 1.48×2?, where x1is the female? athlete’s height? (in inches) and x2is the female? athlete’s percent body? fat, measured as x2?%. Use the multiple regression equation to predict the total body weight for a female athlete who is 61 inches tall and has 30?% body fat.
The predicted total body weight for a female athlete who is 61 inches tall and has 30?%
body fat is
pounds.?
(Round to the nearest tenth as? needed.)