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A true/false test has 90 questions. A passing grade is 59% or more correct answers. Find the approximate probability that a person who is just guessing will pass the test.
$2.00$1.00Question: A true/false test has 90 questions. A passing grade is 59% or more correct answers. Find the approximate probability that a person who is just guessing will pass the test.

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Assume that airplanes land independently of one another on a particular runway. If there is an 8% chance that no airplanes land in an hour, what is the probability that six airplanes land in an hour?
$3.00$2.00Question: Assume that airplanes land independently of one another on a particular runway. If there is an 8% chance that no airplanes land in an hour, what is the probability that six airplanes land in an hour?
A: 0.6188
B: 0.7351
C: 0.1515
D: 0.0288

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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7 years, and standard deviation of 1.6 years.
$3.00$2.00Question: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7 years, and standard deviation of 1.6 years.
If you randomly purchase one item, what is the probability it will last longer than 11 years?

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The waiting time(in minutes) for customers at a driveinbank
$2.00$1.00Question: The waiting time(in minutes) for customers at a driveinbank is an exponentially distributed random variable. The average(mean) time a customer waits is 4 minutes. What is the probability that a customer waits more than 5 minutes?

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In a box of 12 light bulbs, it is known that 5 of them are defective. That is, 5 are defective
$3.00$2.00Question: In a box of 12 light bulbs, it is known that 5 of them are defective. That is, 5 are defective and 7 function properly. We select 2 bulbs from the bag at random, without replacement. Find the probability they both function properly. Show work. Round your answer to 3 decimal places.

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Consider a Poisson distribution with a mean of three occurrences per time period. (a) Write the appropriate Poisson probability function f(x)
$5.00$4.00Question:
Consider a Poisson distribution with a mean of three occurrences per time period.
(a) Write the appropriate Poisson probability function f(x)
(b) What is the expected number of occurrences in four time periods?
(c) Write the appropriate Poisson probability function to determine the probability of x occurrences in four time periods f(x)
(d) Compute the probability of three occurrences in one time period. (Round your answer to four decimal places.)
(e) Compute the probability of twelve occurrences in four time periods. (Round your answer to four decimal places.)
(f) Compute the probability of nine occurrences in three time periods. (Round your answer to four decimal places.)

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A parcel service to establish a weight value c, beyond which there will be an additional charge. The weight of parcels handled by this service is Normally distributed
$2.00$1.00Question: Normal Distribuion Probability
A parcel service to establish a weight value c, beyond which there will be an additional charge. The weight of parcels handled by this service is Normally distributed with a mean of 7 kg and a standard deviation of 2.1 kg.
 What value for c (in kg) will insure that only 2.5% of handled package are assessed the additional charge? (Give decimal answer to two places past decimal.)
 What value for c (in kg) will insure that only 1.0% of the handled packages are assessed the additional charge? (Give decimal answer to two places past decimal.)

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Last month the waiting time at the drive through window of a fastfood restaurant was 3.7 minutes
$2.00$1.00Question:
Last month the waiting time at the drivethrough window of a fastfood restaurant was 3.7 minutes. The franchise has installed a new process intended to reduce waiting time. After the installation, a random sample of 64 orders is selected. The sample mean waiting time is 3.57 minutes with a sample standard deviation of 0.8 minutes. At a 5% level of significance, is there sufficient evidence that the population mean waiting time is now less than 3.7 minutes? What is your conclusion?

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Suppose that 32% of all users the Infinity Affinity Web site drink diet soft drinks regularly
$2.00$1.00Question:
Suppose that 32% of all users the Infinity Affinity Web site drink diet soft drinks regularly. What is the probability that in survey of a randomly selected sample of 200 of the site’s users, the proportion who say that they drink diet soft drinks regularly will be 40% or less? (Show your work. As part of your answer, you should confirm that the sampling distribution of p is approximately Normal.)

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The life in hours of an electronic sensor is known to be approximately Normally distributed
$3.00$2.00Question:
The life in hours of an electronic sensor is known to be approximately Normally distributed, with population standard deviation = hours. A random sample of 10 sensors resulted in the following data: 500,550,560,575,525,505,510,540,550,545.
 Is there evidence to support the claim that mean life exceeds 520 hours? Use a fixedlevel test with alpha = 0.05.
 What is the Pvalue of this test? Conclude the same of part (a)?
 What is the Betavalue for this test if the true mean life is 535 hours?
 What sample size would be required to ensure that Beta does not exceed 0.10 if the true mean life is 540 hours?
 Construct a 95% onesided lower CI on the mean life.
 Use the CI found in part e) to test the hypothesis.

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The waiting time (in minutes) for customers at a driveinbank is an exponentially distributed
$2.00$1.00Question:
The waiting time (in minutes) for customers at a driveinbank is an exponentially distributed random variable. The average(mean) time a customer waits is 4 minutes. What is the probability that a customer waits more than 5 minutes?

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A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with 90 % confidence
$2.00$1.00Question:
A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with 90 % confidence.
a) Assume population standard deviation is known and is equal to 31.
b) Assume that population standard deviation is not known.
47 95 54 33 64 48 57 9 80 8 90 3 49 4 44 79 80 48 16 68 7 15 21 52 6 78 109 40 50 29 5.

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Curing diabetes: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach
$2.00$1.00Question
Curing diabetes: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that greater than 58% of those with diabetes who undergo this surgery will recover from diabetes? Use the a = 0.10 level of significance and the Pvalue method with the TI84 calculator. Source: New England Journal of Medicine 357:753761
State the null and alternate hypotheses.
Но: р (select)______
H1 p (select) ______
This hypothesis test is a (select) test

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A different sample of size n = 20 produced a sample mean of 31.08% and a sample standard deviation of 5.48%.
$2.00$1.00Question:
A different sample of size n = 20 produced a sample mean of 31.08% and a sample standard deviation of 5.48%. Use these values to calculate a 90% confidence interval for the national mean percent of lowincome working families. Please show all calculations and provide the upper and lower limits that make up the confidence interval. (Round the limits to two decimal places).