Statistics

Question 1

1. A standard normal distribution has a mean of _____ and standard deviation of _____.

		zero, zero
		zero, one
		one, one
		one, zero

1 points  

Question 2

1. The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.

		Less than
		Greater than
		Equal to
		A, B, or C above dependent on the value of the mean
		A, B, or C above dependent on the value of the standard deviation

1 points  

Question 3

1. The MPG (Miles per Gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What is the probability that the MPG for a selected mid-size car would be: Less than 33.2?

		43.32%
		6.68%
		93.32%
		86.64%
		13.36%

1 points  

Question 4

1. The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 900 grams?

		4772
		.9772
		.9544
		.0228
		.0456

1 points  

Question 5

1. Which of the following statements is not a property of the normal probability distribution?

		The normal distribution is symmetric.
		95.44% of all possible observed values of the random variable x are within plus or minus three standard deviations of the population mean.
		The mean, median, and mode are equal.
		The area under the normal curve to the right of the mean is equal to the area under the normal curve to the left of the mean.
		All of the above answers are properties of the normal distribution.

1 points  

Question 6

1. For a normal population with a mean of 10 and a variance 4, the P(X ≥ 10) is ___.

		1.0
		0.5
		0.75
		0.25

1 points  

Question 7

1. The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly: Less than 4.66 hours?

		-.0062
		.5062
		.0062
		.9938

1 points  

Question 8

1. What is the probability that a standard normal random variable will be between .3 and 3.2?

		.6179
		.3808
		.6192
		.9987

1 points  

Question 9

1. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. What is the probability that a randomly selected apple will contain between 2.00 and 3.00 ounces?

		.0475
		.4525
		.9525
		.9554

1 points  

Question 10

1. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random from the population is between 30.25 and 30.65 inches long?

		.9987
		.1574
		.1587
		.8413
Question 1 1. (Percentile) An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. 77% of the apples will contain at least how many ounces of juice? 2.12 2.38 2.36 2.14 1 points   Question 2 1. (Percentile) An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. Between what two values (in ounces) symmetrically distributed around the population mean will 80% of the apples fall? [2.13 2.37] [2.10 2.40] [2.06 2.44] [1.95 2.55] 1 points   Question 3 1. (Percentile) Find z when the area between 0 and z is .4750 -1.96 1.96 0.68 -0.68 1 points   Question 4 1. (Percentile) Find z when the area to the right of z is .1314 1.12 0.55 -0.55 -1.12 1 points   Question 5 1. (Percentile) Find z when the area to the left of z is .6700 0.75 0.44 -0.44 -0.75 1 points   Question 6 1. (Percentile) Find z when the area between z and - z is .9030 1.50 1.30 0.12 1.66 1 points   Question 7 1. (Percentile) The average time a subscriber spends reading the local newspaper is 49 minutes. Assume the standard deviation is 16 minutes and that the times are normally distributed. For the 10% who spend the most time reading the paper, how much time do they spend? 11.72 28.52 86.28 69.48 1 points   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. 3.360 3.680 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?

		.03
		.01
		.1732
		.0577
		.10