You were told that the amount of time lapsed between consecutive trades on the N

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. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. 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 between 13 and 16 seconds?

Explanation / Answer

Mean = 15 seconds

lets say standard deviation is = s

so Pr(16 < t< 17 ; 15; s) = 0.13

and Pr(t <13; 15; s) = 0.07

so Pr(t <13; 15; s) = Pr( t >17; 15; s) as the distribution is normal which is symmetric around the mean value 15.

so Pr(13 < t < 16) = 1 - [ Pr(t <13) + Pr( t >16)]

1 - [ Pr(t <13) + Pr (16 <t <17) + Pr( t>17) ]

= 1 - [ 0.07 + 0.13 + 0.07] = 0.73

so, the probability that the time lapsed between two consecutive trades will be between 13 and 16 seconds is 0.73.

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