A CLT tail probability

MediumStatistics~4m

Per-trade P&L is i.i.d. from a skewed, non-Normal distribution with mean $50 and standard deviation $10. Over a day you make $n=100$ independent trades. Using the central limit theorem, estimate the probability that the average P&L per trade exceeds $52. Give a decimal to three places. (Use $\Phi(2)=0.9772$ .)

Show hints (2)+

The CLT makes the sample mean Normal - use SE $=\sigma/\sqrt n=1$ , not $\sigma$ .
$z=(52-50)/1=2$ , then $P(Z>2)=1-\Phi(2)$ .

Answer

Reveal answer →

0.023 (± 0.002)

Create a free account to see the full worked solution and track your progress.

Create a free account

Interview format: Numerical Reasoning Tests, Systematic & Data-Driven Trading

A CLT tail probability

Answer

Related questions