What is the z-score of a value of 27, given a set mean of 24, and a standard deviation of 2?

x = 27 , \$\mu\$ = 24 , \$\sigma\$ = 2

z-score = \$\frac{x- \mu}{\sigma}\$

Put x = 27 in the formula

z-score = \$\frac{27- \mu}{\sigma}\$

Then substract the mean by substitution

z-score = \$\frac{27- 24}{\sigma}\$ = \$\frac{3}{\sigma}\$

Divide the obtained value by standard deviation \$\sigma\$ = 2

z-score = \$\frac{3}{2}\$

z-score at 27

+ 1.5

This indicates that 27 is 1.5 standard deviations above the mean

z-score is positive

Answer

C