Final answer:
The 20% quantile of the N(0,1) distribution is the value below which 20% of the observations lie. For a standard normal distribution, this is a negative z-value found using normal distribution tables or software. The correct answer is b. -0.84, as it represents the 20th percentile value.
Step-by-step explanation:
The question asks which number is closest to the 20% quantile of the N(0,1) distribution, meaning the value below which 20% of observations fall. To find this number, we use the fact that the normal distribution is symmetric about the mean. If we are looking for the 20th percentile, we find the value that leaves 80% of the distribution above it. Since the total area under the distribution is 1, the area in the tail below the 20th percentile is 0.20. We can use normal distribution tables or software to find this value. In the case of N(0,1), we are looking for a negative z-value, since 20% is less than 50% (the mean of the distribution).
The correct answer is b. -0.84, as it is the negative of the 80th percentile value (since it's symmetrical around zero for the N(0,1) distribution). This value represents the point below which approximately 20% of the data in a standard normal distribution would lie.