### CFA Practice Question

There are 985 practice questions for this topic.

### CFA Practice Question

For x, a normal random variable, which of the following is false?

A. P(Q1 < x < Q3) = 50%
B. Q1 is 0.67 standard deviations below the mean.
C. x-score that cuts off the top 10% of the distribution is 1.28 standard deviations below the mean.

The x-score that cuts off the top 10% of the distribution must be above the mean. In fact, the x-score that cuts off the top 10% of the distribution is 1.28 standard deviations above the mean.

User Comment
tenny45 Can someone explain how to get the st.dev of 1.28?
tanyak Confidence interval for the 90th percentile (top 10%) for normal random variable is 1.282. 1.282 is just a number you need to know as it is stated in the text.

95th percentile - 1.65
99th percentile - 2.327

I would memorize these just in case...
sivenkova Why are confidence interval stated differently: in the text it is said 90% - 1.645, not 1.282?
rickeling 1.282 is the square root of 1.645
surob Rickeling, I don't agree with you. I think you cannot take square root of 1.645 because:

1) it is not a varian to take a square root;
2) it simply serves as a multiplier for a standard deviation such as 1.645*standard deviation +/-mean - 90% confidence interval

I think the question is implying that 80% of the x lies within 1.28*s +/-mean. 10% - upper tail of the normal distribution, 10% - lower tail of the normal distribution.
mordja Not to point out the obvious but we know that 50% of the distribution lies above the mean. If a score is below the mean, we know it cuts off >10% of the distribution. The last answer is obviously wrong without needing to calculate.
MFTIOA +- 1.28 =80%
+- 1.65 =90%
+- 1.96 =95%
+- 2.58 =99%

+- 1.00 =68%
TheHTrader And how do you explain "Q1 is 0.67 standard deviations below the mean"?
ngoldstein Quartile 1 is 0.67 Standard deviations below the mean.

Theres no way they don't include a z-table, t-table, chi-square and f-table (if they are required), right?
DonAnd +-(0.67)s.d. = 50%
davcer 99 - 2.58
98- 2.33
95- 1.96
90- 1.65
80- 1.28