Probability-of-normal-distribution-1- -v2

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					              Sub: Statistics                                                                            Topic: Probability


              Find the probability using normal distribution.

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              A citrus farmer has determined that the diameters of its grapefruits are normally distributed
              with a mean of 4.5 inches and a standard deviation of 0.3 inches.

              a. What is the probability that a randomly selected grapefruit will have a diameter of at least
              4.14 inches? __________

              b. What percentage of grapefruits has a diameter between 4.8 and 5.04 inches? __________

              c. The farmer packs its largest grapefruits in special packages called the super pack. If 5 percent
              of all their grapefruits are packed as super packs, what is the smallest diameter of the
              grapefruits that are included? __________

              d. In this year’s harvest, there were 111,500 grapefruits that had a diameter over 5.01 inches.
              How many grapefruits has the grower harvested this year? __________

              e. If we consider that the mean of all grapefruits harvested is 4.5 inches, what is the probability
              that a grapefruit will be exactly 4.5 inches in diameter? __________

              The information given in the problem is represented by the following notations:

              Let the random variable X be the diameter of grapefruits

              Mean diameter of the grape fruit = µ=4.5 inches

              Standard deviation of diameter of the grape fruit =  =0.3 inches

Description: Find the probability using normal distribution.
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