Answer :
Final answer:
The probability that the mean diameter of randomly selected oranges falls between 5.5 and 6.2 inches can be calculated by determining the relevant z-scores and referencing them on a standard normal distribution table.
Explanation:
To find the probability that the mean diameter of randomly selected oranges falls between 5.5 and 6.2 inches, we will consider the given distribution. The mean diameter of oranges in our distribution is 5.85 inches with a standard deviation of 0.24 inches. Therefore, from our question, the diameters of 5 randomly selected oranges form a normal distribution with mean = 5.85 and standard deviation = 0.24/√5.
To calculate the probability, we can use z-scores. A z-score is a measure of how many standard deviations an element is from the mean. For our range of mean diameters, we calculate the z-scores as follows:
Z1 = (5.5 - 5.85) / (0.24/√5)
Z2 = (6.2 - 5.85) / (0.24/√5)
Once we calculate Z1 and Z2, we refer to a Z-table (standard normal distribution table) to find the probabilities corresponding to these z-scores. The probability that the mean diameter of oranges falls between 5.5 and 6.2 would be the probability of Z2 minus the probability of Z1.
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