stastic simple question
jjo030u1.
A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a one-hour flight is 0.073. |
(a) |
What is the probability that both will fail? (Round your answer to 4 decimal places.) |
Probability |
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(b) |
What is the probability that neither will fail? (Round your answer to 4 decimal places.) |
Probability |
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(c) |
What is the probability that at least one fails? (Round your answer to 4 decimal places.) |
Probability |
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2.
A biometric security device using fingerprints erroneously refuses to admit 1 in 1,800 authorized persons from a facility containing classified information. The device will erroneously admit 1 in 1,015,000 unauthorized persons. Assume that 90 percent of those who seek access are authorized. |
If the alarm goes off and a person is refused admission, what is the probability that the person was really authorized? (Round your answer to 5 decimal places.) |
Probability |
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3.
Given P(A) = 0.40, P(B) = 0.50. |
If A and B are independent, find P(A ∩ B). (Round your answer to 4 decimal places.) |
P(A ∩ B) |
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4.
Calculate each binomial probability: |
(a) |
Fewer than 5 successes in 14 trials with a 30 percent chance of success. (Round your answer to 4 decimal places.) |
Probability |
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(b) |
At least 4 successes in 5 trials with a 50 percent chance of success. (Round your answer to 4 decimal places.) |
Probability |
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(c) |
At most 13 successes in 15 trials with a 70 percent chance of success. (Round your answer to 4 decimal places.) |
Probability |
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5.
If arrivals occur at a mean rate of 3.6 events per hour, the exponential probability of waiting less than 0.5 hour for the next arrival is:
.8347.
.8105.
.7809.
.7122.
6.
The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution?
2.0
1.0
1.5
1.2
7.
Which of the following characterizes a Bernoulli process?
A random experiment that has only two outcomes.
The probability of "success" varies with each trial.
Either outcome has the same chance of occurrence.
The "success" must be a desirable outcome.
8.
The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches. What proportion of brook trout caught will be between 12 and 18 inches in length?
.6563
.4082
.2486
.6826
9.
Use Excel to find the critical value of z for each hypothesis test. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.) |
(a) |
10 percent level of significance, two-tailed test. |
Critical value of z |
± |
(b) |
2 percent level of significance, right-tailed test. |
Critical value of z |
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(c) |
1 percent level of significance, left-tailed test. |
Critical value of z |
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10.
Which distribution is most nearly appropriate to describe the number of fatalities in Texas in a given year due to poisonous snakebites?
Poisson
Geometric
Hypergeometric
Binomial
11.
If A and B are mutually exclusive events, then P(A ∩ B) = P(A) + P(B).
True
False
12.
Events A and B are mutually exclusive if P(A ∩ B) = 0.
True
False
13.
The probability of A and its complement (A´) will always sum to one.
True
False
14.
Car security alarms go off at a mean rate of 4.0 per hour in a large Costco parking lot. |
Find the probability that in an hour there will be (Round your answers to 4 decimal places.) |
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Probability |
(a) |
no alarms |
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(b) |
fewer than five alarms |
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(c) |
more than seven alarms |
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15.
On average, 2 percent of all persons who are given a breathalyzer test by the state police pass the test (blood alcohol under 0.08 percent). Suppose that 420 breathalyzer tests are given. |
(a) |
What is the expected number who pass the test? (Round your answer to the nearest whole number.) |
Expected number |
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(b) |
What is the approximate Poisson probability that 5 or fewer will pass the test? (Round your answer to 4 decimal places.) |
Poisson probability |
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[The following information applies to the questions displayed below.]
Historically, 6 percent of a mail-order firm's repeat charge-account customers have an incorrect current address in the firm's computer database. |
The number of customers out of 13 who have an incorrect address in the database is a binomial random variable with n = 13 and π = 0.06. |
rev: 05_22_2012
16.
Required information
(a) |
What is the probability that none of the next 13 repeat customers who call will have an incorrect address? (Round your answer to 4 decimal places.) |
Probability |
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17.
Required information
(b) |
What is the probability that two customer who call will have an incorrect address? (Round your answer to 4 decimal places.) |
Probability |
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18.
Required information
(c) |
What is the probability that three customers who call will have an incorrect address? (Round your answer to 4 decimal places.) |
Probability |
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19.
Required information
(d) |
What is the probability that fewer than four customers who call will have an incorrect address? (Round your answer to 4 decimal places.) |
Probability |
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20.
If the weight (in grams) of cereal in a box of Lucky Charms is N(470,4), what is the probability that the box will contain less than the advertised weight of 458 gm? Note: You may need to use Excel to calculate the exact probabilities. (Round your answer to 5 decimal places.) |
Probability |
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21.
Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.37 claim per month. |
(a) |
What is the probability that the dealership will wait at least 10 months until the next claim? (Round your answer to 4 decimal places.) |
Probability |
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(b) |
What is the probability that the dealership will wait at least a year? (Round your answer to 4 decimal places.) |
Probability |
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(c) |
What is the probability that the dealership will wait at least 2 year? (Round your answer to 4 decimal places.) |
Probability |
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(d) |
What is the probability that the dealership will wait at least 10 months but not more than 1 year?(Round your answer to 4 decimal places.) |
Probability |
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22.
Answer the following: |
a. |
Find the uniform continuous probability for P(X < 22) for U(0, 50). (Round your answer to 4 decimal places.) |
Probability |
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b. |
Find the uniform continuous probability for P(X > 454) for U(0, 1,000). (Round your answer to 4 decimal places.) |
Probability |
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c. |
Find the uniform continuous probability for P(23 < X < 51) for U(20, 69). (Round your answer to 4 decimal places.) |
Probability |
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23.
The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 600 and a standard deviation of 70. |
(a) |
Find the credit score that defines the upper 20 percent. (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) |
Credit score |
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(b) |
Eighty-five percent of the customers will have a credit score higher than what value? (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) |
Credit score |
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(c) |
Within what range would the middle 90 percent of credit scores lie? (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) |
Range |
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to |
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24.
Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 5.9 telephone orders per hour. |
(a) |
Find the probability that at least 37 minutes will elapse before the next telephone order. (Round intermediate values and your final answer to 4 decimal places.) |
Probability |
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(b) |
Find the probability that less than 12 minutes will elapse. (Round intermediate values and your final answer to 4 decimal places.) |
Probability |
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(c) |
Find the probability that between 12 and 37 minutes will elapse. (Round intermediate values and your final answer to 4 decimal places.) |
Probability |
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25.
If arrivals follow a Poisson distribution, waiting times follow the exponential distribution.
True
False
26.
For a continuous random variable, the total area beneath the PDF will be greater than zero but less than one.
True
False
[The following information applies to the questions displayed below.]
Use the sample information = 37, σ = 5, n = 15 to calculate the following confidence intervals for μ assuming the sample is from a normal population. |
27.
Required information
(a) |
90 percent confidence. (Round your answers to 4 decimal places.) |
The 90% confidence interval is from to |
28.
Required information
(b) |
95 percent confidence (Round your answers to 4 decimal places.) |
The 95% confidence interval is from to |
29.
Required information
(c) |
99 percent confidence.(Round your answers to 4 decimal places.) |
The 99% confidence interval is from to |
30.
Required information
(d) |
Describe how the intervals change as you increase the confidence level. |
The interval gets wider as the confidence level decreases. |
The interval gets narrower as the confidence level increases. |
The interval gets wider as the confidence level increases. |
The interval stays the same as the confidence level increases. |
、
[The following information applies to the questions displayed below.]
A random sample of 100 items is drawn from a population whose standard deviation is known to be σ = 50. The sample mean is = 850. |
31.
Required information
(a) |
Construct an interval estimate for μ with 95 percent confidence. (Round your answers to 1 decimal place.) |
The 95% confidence interval is from to |
32.
Required information
(b) |
Construct an interval estimate for μ with 95 percent confidence, assuming that σ = 100. (Round your answers to 1 decimal place.) |
The 95% confidence interval is from to |
33.
Required information
(c) |
Construct an interval estimate for μ with 95 percent confidence, assuming that σ = 200. (Round your answers to 1 decimal place.) |
The 95% confidence interval is from to |
34.
Required information
(d) |
Describe how the confidence interval changes as σ increases. |
The interval stays the same as σ increases. |
The interval gets wider as σ decreases. |
The interval gets wider as σ increases. |
The interval gets narrower as σ increases. |
35.
In constructing a confidence interval for the mean, the z distribution provides a result nearly identical to the t distribution when n is large.
True
False
36.
As n increases, the width of the confidence interval will decrease, ceteris paribus.
True
False
37.
When the sample standard deviation is used to construct a confidence interval for the mean, we would use the Student's t distribution instead of the normal distribution.
True
False
38.
The Central Limit Theorem (CLT) implies that:
repeated samples must be taken to obtain normality.
the mean follows the same distribution as the population.
the population will be approximately normal if n ≥ 30.
the distribution of the mean is approximately normal for large n.
[The following information applies to the questions displayed below.]
GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.6 mg of mercury. A sample of 25 bulbs shows a mean of 3.65 mg of mercury. |
39.
Required information
(a) |
State the hypotheses for a right-tailed test, using GreenBeam’s claim as the null hypothesis about the mean. |
40.
Required information
(b) |
Assuming a known standard deviation of 0.16 mg, calculate the z test statistic to test the manufacturer's claim. (Round your answer to 2 decimal places.) |
Test statistic |
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41.
Required information
(c) |
At the 10 percent level of significance (α = 0.1) does the sample exceed the manufacturer’s claim? |
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42.
Required information
(d) |
Find the p-value. (Round your answer to 4 decimal places.) |
p-value |
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43.
A simultaneous reduction in both α and β will require a larger sample size.
True
False
44.
The least squares regression line is obtained when the sum of the squared residuals is minimized.
True
False
窗体顶端
45.
In a simple regression, if the coefficient for X is positive and significantly different from zero, then an increase in X is associated with an increase in the mean (i.e., the expected value) of Y.
True
False
窗体底端
46.
If R2 = .36 in the model Sales = 268 + 7.37 Ads, then Ads explains 36 percent of the variation in Sales.
True
False
47.
The ordinary least squares regression line always passes through the point .
True
False
48.
In simple linear regression, the coefficient of determination (R2) is estimated from sums of squares in the ANOVA table.
True
False
49.
A prediction interval for Y is narrower than the corresponding confidence interval for the mean of Y.
True
False
50.
When comparing the 90 percent prediction and confidence intervals for a given regression analysis:
the prediction interval is narrower than the confidence interval.
there is no difference between the size of the prediction and confidence intervals.
no generalization is possible about their comparative width.
the prediction interval is wider than the confidence interval.
51.
Which is not true of the coefficient of determination?
It reports the percent of the variation in Y explained by X.
It is calculated using sums of squares (e.g., SSR, SSE, SST).
It is the square of the coefficient of correlation.
It is negative when there is an inverse relationship between X and Y.
窗体顶端
52.
A local trucking company fitted a regression to relate the cost of its shipments as a function of the distance traveled. The Excel fitted regression is shown. Based on this estimated relationship, when distance increases by 50 miles, the expected shipping cost would increase by:
$143.
$286.
$104.
$301.
窗体底端
窗体顶端
53.
If SSR is 2592 and SSE is 608, then:
the standard error would be large.
the coefficient of determination is .81.
the slope is likely to be insignificant.
the SST would be smaller than SSR.
窗体底端