# Mathematics

Question 8

1. (Percentile) The weight of a product is normally distributed with a mean of four ounces and a variance of .25 “squared ounces.” The company wants to classify the unit as a scrap in a maximum of 1% of the units if the weight is below a desired value. Determine the desired weight such that no more than 1% of the units are below it.

 3.36 3.68 2.835 3.418

1 points

Question 9

1. (Percentile) An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed. What raw score corresponds to the 70th percentile?

 77.4 83.5 82.6 76.5

1 points

Question 10

1. (Percentile) During the past six months, 73.2% of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of \$8.22 and a standard deviation of \$1.10. 99% of the households spent less than what amount?

 \$5.66 \$10.78 \$6.81 \$9.63

Question 1

1. For any sampled population, the population of all sample means is approximately normally distributed.

True

False

1 points

Question 2

1. If a population is known to be normally distributed, then it follows that the sample standard deviation must equal σ.

True

False

1 points

Question 3

1. If the sampled population is exactly normal distribution, then the sampling distribution of   is also expected to be normal regardless of the sample size.

True

False

1 points

Question 4

1. The mean of the sampling distribution of   is always equal to the mean of the sampled population.

True

False

1 points

Question 5

1. The central limit theorem states that as the sample size increases the distribution of the sample ________ approach the normal distribution.

 medians means standard deviations variances

1 points

Question 6

1. As the sample size ______________ the variation of the sampling distribution of   ___________.

 Decreases, decreases Increases, remains the same Decreases remains the same Increases, decreases None of the above

1 points

Question 7

1. If the sampled population has a mean 48 and standard deviation 16, then the mean and the standard deviation for the sampling distribution of   for n = 16 are:

 4 and 1 12 and 4 48 and 4 48 and 1 48 and 16

1 points

Question 8

1. A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will exceed 94 lbs. is:

 34.13% 84.13% 15.87% 56.36% 16.87%

1 points

Question 9

1. A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will be less than 84 lbs. is:

 16.87% 93.32% 43.32% 6.678% 84.13%

1 points

Question 10

1. In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process: What is the standard deviation of the sampling distribution of the sample mean?

 0.03 0.01 0.1732 0.0577 0.1

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