# Corresponding z score

Question 1

The shape of a given distribution is normal with a mean of 75 and a standard deviation of 5.5. With these parameters, answer the associated question(s).

For these parameters, transform a raw score of X = 90 into its corresponding z score. Round to the nearest tenths place if a fraction. The z score is:

A.  -2.7

B. -1.6

C.  .1

D.  1.6

E. 2.7

F. the correct z score is a value not listed in alternatives “a” through “e”

Question 2

The Centers for Disease Control & Prevention  in Maryland reports that the mean weight (in pounds) for adult females aged 20 years and over is µ = 166.  Assume that this distribution is normal in shape and the standard deviation = 25.  If you find that a particular woman’s weight given as a z score is z = -1.5, how many pounds does she weigh  (that is, solve for X)? Round to the nearest tenths place if a fraction.  [Note, if your calculated value is not identical to one of the values below, but within plus or minus 0.5 of an answer below, assume it’s a rounding error and select the answer that is closest to your calculated value.]

A. 128.5

B. 164.5

C. 166.5

D.  203.5

E. the correct answer is a value not listed in alternatives “a” through “d”

Question 3

The Centers for Disease Control & Prevention  in Maryland reports that the mean weight (in pounds) for adult females aged 20 years and over is µ = 166.  Assume that this distribution is normal in shape and the standard deviation = 25.  Find the z score for a woman with a weight of 130 pounds (that is, for  X = 130).  Round to the nearest tenths place if a fraction.  [Note, if your calculated value is not identical to one of the values below, but within plus or minus 0.2 of an answer below, assume it’s a rounding error and select the answer that is closest to your calculated value.]

A. +2.3

B. -.7

C.  +.7

D. -1.8

E. the correct z score is a value not listed in alternatives “a” through “d”

Question 4

The shape of a given distribution is normal with a mean of 450 and a standard deviation of 60. With these parameters, answer the associated question(s).

For these parameters, calculate the raw score (X) corresponding to a z score of z = 0.05. Round to the nearest tenths place if a fraction. The X score is:

A. 447

B. 453

C. 456.3

D. 459.6

E. 460

F. the correct X score is a value not listed in alternatives “a” through “e”

Question 5

For a population automobile drives in a medium-sized city (population about 100,000), the traffic police ticketed numerous drivers speeding in school zones during school hours. The drivers’ ticketed speeds formed a normal distribution with a mean of µ = 35 (miles per hour) and ơ = 5. With these parameters, answer the associated question(s).

If someone’s ticketed speed, X, were converted to a z score and that z score equals -.5, how fast was the driver going? Round to the nearest tenths place if a fraction.

A. 22.5

B. 28.5

C. 32.5

D. 37.5

E. 47.5

F. the correct speed is a value not listed in alternatives “a” through “e”

Question 6

The distribution of students’ heights in a class of 100 students is normal, with a mean height of 66 inches and a standard deviation of three. With these parameters, answer the associated question(s).

The shortest 10% of the class is equal to or shorter than __________ inches. Round to the nearest tenths place if a fraction.

A.  58.9

B,  59.9

C. 62.2

D.  67.4

E. the correct value in inches is a value not listed in alternatives “a” through “d”

Question 7

The total number of pages in college textbooks has been found to be a normal shaped distribution  with a mean of µ = 325 pages in length, and a standard deviation = 115.   .  Find the percentage of books that are between 300 and 400 pages in length. Round to the nearest hundredths place if a fraction.  [Note, if your calculated value is not identical to one of the values below, but within plus or minus 0.25 of an answer below, assume it’s a rounding error and select the answer that is closest to your calculated value.]

A.  8.71

B. 24.22

C. 32.93

D. 92.93

E. the correct answer is a value not listed in alternatives “a” through “d”

Question 8

The Centers for Disease Control & Prevention  in Maryland reports that the mean weight (in pounds) for adult females aged 20 years and over is µ = 166.  Assume that this distribution is normal in shape and the standard deviation = 25.  Find the percentage of females who are equal to or below a weight of 110 pounds.  Your answer will be the percentile rank, really, of  X = 110. Round to the nearest hundredths place if a fraction.  [Note, if your calculated value is not identical to one of the values below, but within plus or minus 0.25 of an answer below, assume it’s a rounding error and select the answer that is closest to your calculated value.]

A. 1.25

B.  2.24

C.  48.75

D. 98.75

E. the correct answer is a value not listed in alternatives “a” through “d”

Question 9

For a population automobile drives in a medium-sized city (population about 100,000), the traffic police ticketed numerous drivers speeding in school zones during school hours. The drivers’ ticketed speeds formed a normal distribution with a mean of µ = 35 (miles per hour) and ơ = 5. With these parameters, answer the associated question(s).

What is the speed someone was driving where 40 percent of the ticketed drivers were driving at or below this speed? Round to the nearest tenths place if a fraction.

A. 30

B.  33.75

C. 36.3

D. 37.8

E. 47.5

F. the correct speed is a value not listed in alternatives “a” through “e”

Question 10

The shape of a given distribution is normal with a mean of 450 and a standard deviation of 60. With these parameters, answer the associated question(s).

For these parameters, calculate the raw score (X) corresponding to a z score of z = 1.65. Round to the nearest tenths place if a fraction. The X score is:

A.  439

B. 458

C. 519

D.  538.5

E. 549

F. the correct X score is a value not listed in alternatives “a” through “e”