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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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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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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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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.