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n = 36
are drawn.
(a) Describe the x distribution
and compute the mean and standard deviation of the distribution.
x has a normal a Poisson a geometric an unknown an approximately normal a binomial
distribution with mean μx = ____
and standard deviation σx = ____ .
(b) Find the z value corresponding to x = 49.
z = ______
(c) Find P(x < 49).
(Round your answer to four decimal places.)
P(x < 49) = ___________
(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 49? Explain.
Yes, it would be unusual because more than 5% of all such samples have means less than 49.
No, it would not be unusual because less than 5% of all such samples have means less than 49.
Yes, it would be unusual because less than 5% of all such samples have means less than 49.
No, it would not be unusual because more than 5% of all such samples have means less than 49.
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2) Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 74 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 74 tons and standard deviation σ = 1.1 ton.
(a) What is the probability that one car chosen at random will have less than 73.5 tons of coal? (Round your answer to four decimal places.)
_________________________
(b) What is the probability that 33 cars chosen at random will have a mean load weight x of less than 73.5 tons of coal? (Round your answer to four decimal places.)
____________________
(c) Suppose the weight of coal in one car was less than 73.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?
Yes
No
Suppose the weight of coal in 33 cars selected at random had an average x of less than 73.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?
Yes, the probability that this deviation is random is very small.
Yes, the probability that this deviation is random is very large.
No, the probability that this deviation is random is very small.
No, the probability that this deviation is random is very large.
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3) Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6150 and estimated standard deviation σ = 1550. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.
(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)
___________________
(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?
The probability distribution of x is not normal.
The probability distribution of x is approximately normal with μx = 6150 and σx = 1096.02.
The probability distribution of x is approximately normal with μx = 6150 and σx = 775.00.
The probability distribution of x is approximately normal with μx = 6150 and σx = 1550.
What is the probability of x < 3500? (Round your answer to four decimal places.)
_____________________
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
__________________
(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?
The probabilities stayed the same as n increased.
The probabilities increased as n increased.
The probabilities decreased as n increased.
If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?
It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.
It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.
It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.
It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.
Question
excavation site. Assume that the population of x values has an approximately normal distribution.
1222 1306 1187 1299 1268 1316 1275 1317 1275
(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)
x =______ A.D.
s = ___________yr
(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)lower limit ______A.D.
upper limit ___________- A.D.
——————
2.
A poll asked the question, “What do you think is the most important problem facing this country today?” Seventeen percent of the respondents answered “crime and violence.” The margin of sampling error was plus or minus 2 percentage points. Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond “crime and violence” to the question asked by the pollsters.
lower limit _______ %
upper limit ________ %
——————–
3.
What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)
(a) a preliminary estimate for p is 0.21
____________
(b) there is no preliminary estimate for p
____________
___________________________
4)
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
In a random sample of 66 professional actors, it was found that 41 were extroverts.
(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)
___________
(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)
lower limit________
upper limit ________
Give a brief interpretation of the meaning of the confidence interval you have found.
We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.
We are 95% confident that the true proportion of actors who are extroverts falls within this interval.
We are 5% confident that the true proportion of actors who are extroverts falls within this interval.
We are 5% confident that the true proportion of actors who are extroverts falls above this interval.
(c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.
No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.
No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.
_____________________
5.
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
A random sample of 5300 permanent dwellings on an entire reservation showed that 1669 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)
lower limit _________
upper limit___________
Give a brief interpretation of the confidence interval.
1% of the confidence intervals created using this method would include the true proportion of traditional hogans.
99% of the confidence intervals created using this method would include the true proportion of traditional hogans.
1% of all confidence intervals would include the true proportion of traditional hogans.
99% of all confidence intervals would include the true proportion of traditional hogans.
(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.
No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.
No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.
Question
has vertices P(−6,2)
P-6,2, A(−3,3)
A-3,3, T(0,2)
T0,2, and H(−3,1)
H-3,1, and then find the perimeter and area of the polygon.
Question 2:
Identify the polygon that has vertices J(12,−4)
J12,-4, U(0,−4)
U0,-4, S(4,3)
S4,3, and T(8,3)
T8,3, and then find the perimeter and area of the polygon.
Question 3:
Identify the polygon that has vertices A(−10,−1)
A-10,-1, P(−7,3)
P-7,3, E(−3,0)
E-3,0, and X(−6,−4)
X-6,-4, and then find the perimeter and area of the polygon.
Question 4:
Identify the polygon with vertices K(0,1)
K(0,1), L(2,−4)
L(2,-4), M(−3,−2)
M(-3,-2), and N(−5,3)
N(-5,3), and then find the perimeter and area of the polygon.
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