Scores on a test are normally distributed with a mean of 76 and a standard deviation of 6. Using the z-score table, estimate the probability a randomly selected student scored below a 64.

Question

a. 

1.2

b. 

0.02

c. 

-0.02

d. 

0.98

Answer 1

b. .02

any probability is between 0 and 1, so you can eliminate a) and c)

you don't need a z table. Just use the empirical rule 68-95-99.7

95% of all data fall within 2 standard deviations of the mean. That leaves 1-.95 = .05 in the tails. .05/2 = .025 in each tail.

the correct answer is .025. round it down and it's .02

76 - 64 = 12. 12/6 = 2 standard devations from the mean

but go on line and there's several websites with z tables and z calculators. Just google "z table"

the z table will give a more accurate decimal place. but regardless of rounding errors .02 is the best answer of the four choices.