# Level 1 - Volume 1 - Reading 10

Can somebody pls help me with question number 10 at the end of Reading 10 (Sampling and Estimation)? I don’t seem to be able to work out the answer to the question 10 a). I have no idea where they got the results from. Cheers, MK

Post the question, you might more responses that way.

The question is as follows: An exchange rate has a given exptected future value and standard variation. Assuming that the exchange rate is normally distributed, what are the probabilities that the exchange rate will be at least 1, 2, or 3 standard deviations away from its mean?

check ur ztables…a normal distribution is the same as standard and they are just a collection of statistical results… shld be in the neighborhood of 99.5…I may not b accurate

Well, that’s the thing. I’ve done that but the results are completely different. Probability of an exchange rate being at least 1 s away from its mean = 0.3174 Probability of an exchange rate being at least 2 s away from its mean = 0.0456 Probability of an exchange rate being at least 3 s away from its mean = 0.0026 I am lost on this one.

i don’t get the 3 SD away one but the first two make sense. prob of being within 1 SD = roughly 68% so 1-.68 = .32 prob of being within 2 SD = roughly 95% so 1-.95 = .05 small differences because Z table values are not exactly .68 and .95

Would the answer be really that easy cos that’s what I did as a first thing? Then I decided to look in the Z tables for the exact values or anything closer to what they used as results but I couldn’t see anything I could use. Thanks guys.

Yes, the question makes sense. The probability of the exchange rate being less than (or equal to) one, two and three SDs away from the expected future value are the probabilities of one, two and three standard deviations away from the mean of a normal distribution, i.e. 68.27%, 95.45% and 99.73%. Hence, we are asked to calculate the probability of being at least this amount away, so you take 1 minus these values. This will give you 31.73%, 4.55% and 0.27% (close enough to the answers above). Hope that helps.

Right. So the issue here is rounding the numbers… I get it. I thought I was going mad. Thank you so much! MK