Question

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be longer than 17 seconds?

Answer 1

Answer:

Step-by-step explanation:

Given that that (X) the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.

i.e. X is normal with mean = 15 and unknown std deviation $\sigma$

Given that$P(X$

i.e. P($z$

z=-1.475 (from normal table)

Hence $\frac{13-15}{\sigma}=-1.475\\\sigma = 1.356$

Using this we find P(X>17) = $P(Z>\frac{17-15}{1.356} \\=P(Z>1.475)\\=0.5-0.428\\=0.072$