Answer :
Final answer:
Without the mean and standard deviation, we cannot calculate the exact probability for the circumference of a regulation soccer ball. If we had these values, we would use z-scores and a standard normal distribution to find the required probability.
Explanation:
The question asks about the probability that a randomly selected regulation soccer ball has a circumference between 66.9 and 68.9 cm. To provide an answer, we would typically use the properties of the normal distribution, given that the circumference of soccer balls follows a normal distribution as per the regulations. However, without specific mean and standard deviation values for the circumference of regulation soccer balls, we can't calculate an exact probability. Instead, if we had comparable data for soccer balls like the example provided for golf scores, we could use z-scores and a standard normal distribution table to find the probability corresponding to the range between two circumferences. In the provided example, to calculate the likelihood that a golfer scored between 66 and 70, we would:
- Calculate the z-score for both values (66 and 70), subtracting the mean (68) and dividing by the standard deviation (3).
- Consult a standard normal distribution table (or a calculator with statistical functions) to find the area under the curve between the two z-scores.
- The area represents the probability of a golfer scoring within that range. For soccer balls, a similar process would apply once the mean and standard deviation of the circumference are known.
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