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The distribution of heights of adult men is Normal, with a mean of 69 inches and a standard deviation of 2 inches. Billy’s height has a z-score of - 0.5 (or negative 0.5) when compared to all adult men. Interpret what this z-score tells about how Billy compares to other men in terms of height.

Question 3 options:

	Billy is less than 69 inches tall.
	Billy is half of a standard deviation below the mean.
	Billy is 68 inches tall.
	All of the above

Question 4 (1 point)

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A cereal manufacturer has a machine that fills the boxes. Boxes are labeled “16 ounces”, so the company wants to have that much cereal in each box, but since no packaging process is perfect, there will be minor variations. If the machine is set at exactly 16 ounces and the Normal model applies, then about ½ the boxes will be underweight, making consumers unhappy and exposing the company to bad publicity and possible lawsuits. To prevent underweight boxes, the manufacturer has to set the mean a little higher than 16 ounces. Specifically, this machine fills boxes according a N(16.5, 0.3) normal model. Use this model to answer the following question.

What percent of boxes will be underfilled (i.e. less than 16 ounces) using this setting for the machine? Choose the range that contains the correct answer.

Question 4 options:

	Between 3% and 4%.
	Between 4% and 5%.
	Between 5% and 6%.
	Between 6% and 7%.
	Between 7% and 8%.

Question 5 (1 point)

A cereal manufacturer has a machine that fills the boxes. Boxes are labeled “16 ounces”, so the company wants to have that much cereal in each box, but since no packaging process is perfect, there will be minor variations. If the machine is set at exactly 16 ounces and the Normal model applies, then about ½ the boxes will be underweight, making consumers unhappy and exposing the company to bad publicity and possible lawsuits. To prevent underweight boxes, the manufacturer has to set the mean a little higher than 16 ounces. Specifically, this machine fills boxes according a N(16.5, 0.3) normal model. Use this model to answer the following question.

How full does a box have to be to be in the top 12% of heaviest boxes? Choose the range that contains the correct answer.

Question 5 options:

	Between 16.5 and 16.6 ounces.
	Between 16.6 and 16.7 ounces.
	Between 16.7 and 16.8 ounces.
	Between 16.8 and 16.9 ounces.
	Between 16.9 and 17.0 ounces.

Question 6 (1 point)

A cereal manufacturer has a machine that fills the boxes. Boxes are labeled “16 ounces”, so the company wants to have that much cereal in each box, but since no packaging process is perfect, there will be minor variations. If the machine is set at exactly 16 ounces and the Normal model applies, then about ½ the boxes will be underweight, making consumers unhappy and exposing the company to bad publicity and possible lawsuits. To prevent underweight boxes, the manufacturer has to set the mean a little higher than 16 ounces. Specifically, this machine fills boxes according a N(16.5, 0.3) normal model. Use this model to answer the following question.

What the probability that a randomly selected box will have a weight between 16 and 16.5 ounces? Choose the range that contains the correct answer.

Question 6 options:

	Between 0.4 and 0.425
	Between 0.425 and 0.45
	Between 0.45 and 0.475
	Between 0.475 and 0.5
	Between 0.5 and 0.525

Question 7 (1 point)

A cereal manufacturer has a machine that fills the boxes. Boxes are labeled “16 ounces”, so the company wants to have that much cereal in each box, but since no packaging process is perfect, there will be minor variations. If the machine is set at exactly 16 ounces and the Normal model applies, then about ½ the boxes will be underweight, making consumers unhappy and exposing the company to bad publicity and possible lawsuits. To prevent underweight boxes, the manufacturer has to set the mean a little higher than 16 ounces. Specifically, this machine fills boxes according a N(16.5, 0.3) normal model. Use this model to answer the following question.

What the probability that a randomly selected box will weight more than 17.4 ounces?

Question 7 options:

	0.0004
	0.0005
	0.0008
	0.0013
	0.005

Answer 1