Final Answer:
-0.842, is the closest to our calculated z-score of approximately -0.8416. Therefore, the correct answer is C) -0.842.
Step-by-step explanation:
To solve this question, we're looking for a z-score where the area to the left of it under the standard normal distribution curve is about 0.2.
The z-score is a statistical measurement that tells us how many standard deviations a data point is from the mean in a normal distribution.
Since a normal distribution is symmetric, and the midpoint (which is the mean in a standard normal distribution) has an area of 0.5 to the left of it, a z-score related to an area of 0.2 will be negative, as it's left of the mean.
Using statistical tables or a calculator with statistical functions, we can find the z-score that corresponds to the left-tail area of 0.2.
After checking the tables or using a relevant function on a statistical calculator, we find that the z-score with a cumulative probability of about 0.2 is -0.8416 when rounded to four decimal places.
Looking at our available options, we must choose the one that is closest to this z-score:
A) -2.054
B) 0.842
C) -0.842
D) 2.054
Option C, which is -0.842, is the closest to our calculated z-score of approximately -0.8416. Therefore, the correct answer is C) -0.842.