In 2002 IAAF (The Federation of Athletics track Events) policies considered that there should be a limit to how fast a human can react to a start signal. In fact, they determined that if an athlete left the blocks sooner than 100 ms after the start signal, he would be deemed to have false-started1. In a 100 metre Sprint the reaction time can be measured in micro seconds using technology, hence, it can be measured if an athlete has had a false-start quite precisely. The following are the procedures for a runner’s reaction;

Gun goes off

Sound travels from gun to ear

Ear registers sound, sends impulse to brain

Brain processes sound, sends signal to start running.

Signal is received by muscles; sprinter goes

On Olympic track in 2003, for example, Jon Drummond refused to leave the track while he had been disqualified because of leaving the block too early by a reaction time of 53ms2. Simplistically this meant that he would have anticipated the gunfire and started the race before the gun went off and thus, he was disqualified and rejected.

Our prediction based on the information above is that it is very unlikely for someone to have to have a reaction time of less than 100 ms. The average human reaction time is given in the task sheet with the mean 215 ms with a standard deviation of 34 ms based on which Jon’s reaction of 53 ms was disqualified.

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Aim

The aim of this investigation, therefore, is to determine whether a human reaction time of faster than 100 ms is a fair benchmark using some Mathematical techniques including; Normal distribution, Central Limit Theorem and 95% Confidence Interval formula for the measurements and calculations in order to check whether Jon Drummond’s claim was justified.

Method

Tit is claimed that the true Mean of the population µ = 215 ms (3sf) and the standard deviation of the population. σ = 34ms (task sheet)

The probability (Pr X≤100) and (Pr X≤53) by putting them into a normal distribution formula. ∴ = 3.60 3sf = 1.37 3sf

A z-score using the IAFF mean, standard deviation and Jon’s reaction time is constructed below. Applying the Z -score formula and graph enable us to compare the data more clearly.. ∴ =-3.380 = -4.760

=-3.380

= -4.760

From the calculation above it can be concluded that the probability of an individual having a reaction time given by (IAFF) of less than or equal 100 ms is 3.60 x 10-4 with a Z-score of =-3.380 which is almost three and half standard deviation below the mean. Hence, knowing that almost more than 99% of the data lies between 3 standard deviation of the mean the reaction time of 100 ms is already a weak probability. Also the probability including Jon’s reaction time which is equal or less than 53 ms , is 1.37 x 10 -8 with a Z-score of = -4.760 which is almost 5 standard deviation below the mean which is even a very highly unlikely probability. This calculations of the probabilities suggests that it is almost impossible to have a reaction time of 100 ms for human let alone to having a reaction of 53 ms.

Reaction time of sample of 5

The following calculations are based on a sample size of 5 reaction time that I have done from the Human Reaction Time on the website provided in the task sheet3 to continue the investigation by using our own data .

The following formula are used to obtain the sample mean and standard deviation. ∴ 15.2 ms

∴247.8 ms (248 3fig). by using cal.

The reaction mean was 248 which is higher than the true mean of the population. Based on central theorem the mean of the sample…