Module 2 Exercise 3

What is the mean of the standard normal distribution?

If a raw score has a z-score of 2.75, then where is it found with respect to the mean?

• above the mean

• below the mean

• it is the mean

• it is the value closest to the mean

What is the z-score equivalent of 68 if

 $\mu=74$ and  $\sigma=4$  ?

What is the z-score equivalent of 63 if

 $\overline{x}=61$   and  $s=3.2$  ?

• 0.625

• -0.625

• 0.635

• -0.635

How many standard deviations is 77 from

 $\mu=81$  if  $\sigma=5$  ?

• 0.8 standard deviations below the mean

• 0.8 standard deviations above the mean

• -0.8 standard deviations below the mean

• -0.8 standard deviations above the mean

How many standard deviations is 95 from 

 $\overline{x}=89$  if  $s=1.5$ ?

• 3.75 standard deviations above the mean

• 3.75 standard deviations below the mean

• 4 standard deviations above the mean

• 4 standard deviations below the mean

The weekly income of managers in a certain company is normally distributed with a mean of P50,000 and a standard deviation of P5,000. What is the z-score for a weekly income of P58,000?

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CCSS.HSS.ID.A.4

The average male foot length is 11 inches with a standard deviation of 1.5 inch. Carlo's foot length is 13.25 inches. What is the z-score equivalent of this?

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CCSS.HSS.ID.A.4

The average female foot length is 9.5 inches with a standard deviation of 1.2 inch. Ciara's foot length is 11.6 inches. What is the z-score equivalent of this?

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CCSS.HSS.ID.A.4

The average male foot length is 11 inches with a standard deviation of 1.5 inch. The average female foot length is 9.5 inches with a standard deviation of 1.2 inch. Carlo's foot length is 13.25 inches, while Ciara's foot length is 11.6 inches. Which of the two has a longer foot relative to his or her gender group?

• Ciara

• Carlo

• It cannot be determined.

• Both of them

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CCSS.HSS.ID.A.4