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stats 1200 quiz 4 ( ch. 14, 19,20)
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Terms in this set (17)
Probability is a measure of how likely an event is to occur. Match one of the probabilities that follow with each statement of likelihood given. Type the correct letter in each box. You must get all of the answers correct to receive full credit. (Into each blank you should type **
CAPITAL LETTER ONLY
** . Do not type in periods or other punctuation.)
1. This event will occur a little less than half the time over a long sequence of trials.
2. This event is impossible. It will never happen.
3. This event is very likely to occur, but is not certain to occur.
4. This event will occur a little more often than not.
1. )0.4
2.)0
3.)0.97
4.)0.55
If the knowledge that an event A has occurred implies that a second event B cannot occur, then the events A and B are said to be
If event A and event B are as above and event A has probability 0.5 and event B has probability 0.2, then the probability that A or B occurs is
mutually exclusive.
0.7
Government data assign a single cause for each death that occurs in the United States. (Thus, in government terminology, causes of death are mutually exclusive.) In a certain city, the data show that the probability is 0.37 that a randomly chosen death was due to cardiovascular (mainly heart) disease, and 0.15 that it was due to cancer.
(a) The probability that a death was due either to cardiovascular disease or to cancer is
(b) The probability that the death was not due to either of these two causes is
A.) 0.52
B.) 0.48
For a particular large group of people, blood types are distributed as shown below. (Note that each person is classified as having exactly one of these blood types.)
Blood Type O A B. AB Probability0.18 0.35 0.05 ?
(a) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly selected person will be able to donate blood to Maria?
(b) If two people are selected at random, what is the probability that both people selected will have type O blood?
c) The probability that a randomly selected person will have type AB blood is
A.) 0.23
B.) 0.0324
C.)0.42
Came with graph screen shot
At a certain high school, if a student is selected at random and asked what they plan to do after graduating, the probability distribution for their response is given above. Determine the following:
(a) P(Receive some sort of formal training after high school) ==
(b) P(Attend a college) ==
(c) P(Attend a junior college) ==
A.) 0.5
B.) 0.3
C.) 0.2
screenshot graph
Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. (You may assume that students are studying at most one language besides English.) Here is the distribution of the students:
Language Spanish French German All Others None Probability 0.290.10.030.030.55
(a) What is the probability that a randomly chosen student is, in fact, studying a language other than English? ANSWER
(b) What is the probability that a randomly chosen student is studying French, German, or Spanish? ANSWER
(c) What is the probability that a randomly chosen student is studying a language besides English, but not German? ANSWER
A.) 0.45
B.) 0.42
C.) 0.42
Suppose that, for students who are enrolled in college algebra, 72 percent are freshmen, 44 percent are female, and 28 percent are female and are freshmen. Your answers below should be entered as decimals and rounded to three decimal places.
(a) One student will be selected at random. What is the probability that the selected student will be a freshman or female (or both)?
(b) One student will be selected at random. What is the probability that the selected student will not be a freshman?
(c) Two students will be independently selected at random. What is the probability that both of the selected students will be female?
A.) 0.88
B.) 0.28
C.) 0.1936
In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 65 percent BLUE, 21 percent RED, and 14 percent GREEN.
Note: Your answers should be rounded to three decimal places.
(a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is the probability that we will spin the wheel exactly three times?
(b) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on RED. What is the probability that we will spin the wheel at least three times?
(c) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on GREEN. What is the probability that we will spin the wheel 2 or fewer times?
A.) 0.0796
B.) 0.624
C.)0.260
The home states of a certain group of people are distributed as follows: 54 percent are from MISSOURI, 27 percent are from KANSAS, and 19 percent are from IOWA. (No one in the group had a home state other than one of these three.)
(Note: Your answer to the question below should be rounded to three decimal places.)
Suppose we randomly select a person from this group. What is the expected value of the number of letters in the selected person's home state?
6.7
A phone-in poll conducted by a newspaper reported that 60% of those who called in liked ''reality TV.''
(a) The unknown true percentage of American citizens who like ''reality TV'' is
(b) The number 60% is a
A.) Parameter
B.) statistic
For the following problems, select the best response.
(a) An estimator is
(b) The sampling distribution of a statistic is
(c) The population is
A.) a statistic that is used to ''guess'' the value of a parameter.
B.) the population consisting of all the values of the statistic that could be observed based on all possible samples of the correct size.
C.)the set of all items of interest.
A measurement is normally distributed with 𝜇=20.5μ=20.5 and 𝜎=5.3σ=5.3. Round answers below to three decimal places.
(a) The mean of the sampling distribution of 𝑥¯x¯ for samples of size 8 is:
(b) The standard deviation of the sampling distribution of 𝑥¯x¯ for samples of size 8 is:
A.) 20.5
B.) 1.874
For patients who have been given a diabetes test, blood-glucose readings are approximately normally distributed with mean 129 mg/dl and a standard deviation 8 mg/dl. Suppose that a sample of 3 patients will be selected and the sample mean blood-glucose level will be computed.
Enter answers rounded to three decimal places.
According to the empirical rule, in 95 percent of samples the SAMPLE MEAN blood-glucose level will be between the lower-bound of and the upper-bound of .
Lower : 119.762
Upper: 138.238
A biologist claims that nearly 45 percent of all Americans have brown eyes. A random sample of 𝑛=80n=80 Mizzou students found 24 with brown eyes. Give the numerical value of the statistic 𝑝̂p^. (Enter you answer as a decimal rounded to three decimal places.) 𝑝̂=p^=
p= 0.3
) Nationwide, 50 percent of persons taking a certain professional certification exam pass. Consider, for a samples of 200, the sampling distribution of 𝑝̂p^. (Each answer should be entered as a proportion rounded to three decimal places.)
(a) The mean of the sampling distribution of 𝑝̂p^ is:
(b) The standard deviation of the sampling distribution of 𝑝̂p^ is:
A.) 0.5
B.) 0.035
A random sample of 80 Mizzou students showed that 24 had driven a car during the day before the survey was conducted. Suppose that we are interested in forming a 99 percent confidence interval for the proportion of all Mizzou students who drove a car the day before the survey was conducted.
Where appropriate, express your answer as a proportion (not a percentage). Round answers to three decimal places.
(a) The estimate is: .
(b) The standard error is:
(c) The multiplier is:
A.)0.3
B.) 0.051
C.) 2.576
A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not. Determine a 80 % confidence interval for the population proportion of college seniors who plan to attend graduate school. (Enter each answer rounded to three decimal places.)
80 % CI: to
0.149 to 0.251
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Verified questions
PROBABILITY
Consider the two samples shown here: Sample 1: 20, 19, 18, 17, 18, 16, 20, 16 Sample 2: 20, 16, 20, 16, 18, 20, 18, 16 (a) Calculate the range for both samples. Would you conclude that both samples exhibit the same variability? Explain. (b) Calculate the sample standard deviations for both samples. Do these quantities indicate that both samples have the same variability? Explain. (c) Write a short statement contrasting the sample range versus the sample standard deviation as a measure of variability.
PROBABILITY
Two different plasma etchers in a semiconductor factory have the same mean etch rate μ. However, machine 1 is newer than machine 2 and consequently has smaller variability in etch rate. We know that the variance of etch rate for machine 1 is $σ^2_1$, and for machine 2, it is $σ^2_2 = aσ^2_1$. Suppose that we have $n_1$ independent observations on etch rate from machine 1 and $n_2$ independent observations on etch rate from machine 2. a. Show that μ = α $μ=α\overline{\text{x}}_1+(1 - α)\overline{\text{x}}_2$ is an unbiased estimator of μ for any value of α between zero and one. b. Find the standard error of the point estimate of μ in part (a). c. What value of α would minimize the standard error of the point estimate of μ?
STATISTICS
Assume that women have diastolic blood pressure measures that are normally distributed with a mean of 70.2 mm Hg and a standard deviation of 11.2 mm Hg. Find the probability that a randomly selected woman has a normal diastolic blood pressure level, whi ch is below 80 mm Hg.
STATISTICS
Consider the following results for independent samples taken from two populations. $$ \begin{array} { l l } { \text { Sample } 1 } & { \text { Sample } 2 } \\ { n _ { 1 } = 400 } & { n _ { 2 } = 300 } \\ { \overline { p } _ { 1 } = .48 } & { \overline { p } _ { 2 } = .36 } \end{array} $$ a. What is the point estimate of the difference between the two population proportions? b. Develop a 90% confidence interval for the difference between the two population proportions. c. Develop a 95% confidence interval for the difference between the two population proportions.
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