### 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 Contributed Comments11

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