Comparing Data Z Score

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

• 2.26

• 16.45

• -2.26

• 1.26

Find the Z-score.

Mean = 21

Standard Deviation: 1.3

x = 22

• 0.77

• 5.33

• 1.07

• 1.26

The sign of the z-score indicates whether the location is above(positive) or below(negative) the mean.

• True

• False

Find the z-scores value corresponding if the location is above the mean by 1/2 standard deviations

• -0.50

• +1.00

• +0.50

• -1.00

If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2.5 inches, what is the z score of a 3rd grader who is 47 inches tall? 

• -5
• -2
• 2
• 5

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval? 

• 1084 to 1216 pounds 
• 1106 to 1150 pounds 
• 1106 to 1194 pounds 
• 1128 to 1172 pounds

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

•  28,000 km and 32,000 km.
• 24,000 km and 34,000 km.
• 26,000 km and 34,000 km.
• 27,000 km and 31,000 km.

A scientist planted two groups of seedlings. After six months, she found that the heights for both groups were normally distributed with means and standard deviations as follows:

Group A: Mean = 41.7 cm, Standard Deviation = 2.2 cm

Group B: Mean = 38.6 cm, Standard Deviation = 3.4 cm

For which group does a z-score of 1.5 give a taller plant?

• Group A - 45 cm

• Group A - 43.2 cm

• Group B - 43.7 cm

• Group B - 42 cm

Researchers in an early childhood development organization investigated the number of words in the vocabularies of young children. Here are some summary statistics:

18 months, mean = 85 words, standard deviation = 80 words

24 months, mean = 275 words, standard deviation = 120 words

Miku (who is 18 months old) has a vocabulary of 93 words, while Tessa (who is 24 months old) has a vocabulary of 287 words.

Relative to their age, who has a larger vocabulary?

• Miku

• Tessa

• Miku and Tessa have equally sized vocabularies relative to their ages.

• It's impossible to say without seeing all of the individual vocabulary sizes.

Jar candle, mean = 25 hours, standard deviation = 2.5

Pillar candle, mean = 95 hours, standard deviation = 7.5

Fezzik has one of each type of candle. He knows his candles each have a z-score of 1.5. How long will each candle burn?

• Jar candle 25 hours, Pillar candle 95

• Jar candle 28.75 hours, Pillar candle 106.25

• Jar candle 27.5 hours, Pillar candle 102.5