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Suppose apples have a mean of 0.75 lbs and a standard deviation of 0.1 lbs. Suppose oranges have a mean of 0.8 lbs and a standard deviation of 0.15 lbs. If you have an apple that weighs 0.9 lbs and an orange that weighs 0.95 lbs, which is heavier, relatively speaking?

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Answer:

Oranges

Explanation:

Let the system be normally distributed.

For apples : mean = 0.75

                    deviation = 0.1 lbs

probability that apples weighs more than 0.9 lbs

                                  = P (Z≥[tex]\frac{0.9-0.75}{0.1}[/tex])

                                  = P (Z≥1.5)

                                 =  1 - 0.9332

                                 = 0.0668

For oranges: mean = 0.8

                    deviation = 0.15 lbs

probability that apples weighs more than 0.95 lbs    

       P (Z≥ (0.95-0.8)/0.15)

           = P (Z≥1)    

           = 1 - 0.8413

           = 0.1587

Based on the probabilities, the orange is greater than the apple so it will weigh more.    

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