Two students calculated a z-value for the 5 inches: z = (desired value minus the
ID: 3124266 • Letter: T
Question
Two students calculated a z-value for the 5 inches: z = (desired value minus the mean) divided by the standard deviation. With this z-value they went to the z-score Table and got an area to the left.
For the quarters this was z = (5 inches - 4.9)/8,76 = 0.011 Then from the Table this corresponded to an area to the left of 0.5040 or 50% The relative frequency, however was 53/180 = 0.29 = 29%.
For the dime is was z = (5 - 7.39)/8.96 = -0.27 and that area from the Table is 0.3936 or 39%. The rel frequency calculation gave 179/300 = 59.6%
WHY THE DISCREPANCY BETWEEN THESE RESULTS FOR THE TWO COINS? IT'S BASIC.
Explanation / Answer
The Statistical definition of probability says that relative frequency converges to probabability in long run. An individual experiment may give an outcome highly deviated from the theoretical probability. If you run the experiment for a large number of times, the relative frequency may get close to the theoretical value of probability.
Tossing a coin is a Bernoulli trial. If you toss the coin n times the number of heads would follow binomial distribution. Binomial distribution can be approximated to normal distribution when n is large. But here the experiment you described may consist of a small number of trials, not leading the binomial distribution into normal distribution. This can be another reason that the probabilities differ from the actual outcome.
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