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golf balls shall not be greater than 1.620 ounces (45.93) the diameter of the ball shall be less than 1.680 inches the velocity f the ball shall not be greater than 250 feet per second. they check these often using random sampling, the dozen of each kind are sampled and if more than three do not meet size, velocity requirements than that kind of ball is removed from their list. what assumptions must be made in order to use binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed? and what information must be know in order to use binomial probability distribution to be able to calculate that particular kind of golf ball will be removed
I doubt if anyone here knows that qnt/561 is a U. of Phoenix statistics class.
To use the binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed, the following assumptions must be made:
1. Each inspection of a dozen golf balls is independent of the others.
2. The probability of a golf ball meeting the size and velocity requirements is the same for each inspection.
3. The sample size of a dozen golf balls is fixed and does not change.
4. The outcome of each inspection is either a success (meeting the requirements) or a failure (not meeting the requirements).
5. The probability of success remains constant throughout the inspections.
To calculate the probability, you would need to know the following information:
1. The total number of golf balls inspected.
2. The number of golf balls meeting the size and velocity requirements in a dozen.
3. The probability of a single golf ball meeting the size and velocity requirements.
With this information, you can calculate the binomial probability using the formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of exactly k successes (k balls do not meet the requirements)
- C(n, k) is the combination formula (n choose k)
- p is the probability of a single golf ball meeting the requirements
- n is the total number of golf balls inspected
- k is the number of golf balls that do not meet the requirements