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

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```					              Sub: Statistics                                                                            Topic: Probability

Question:

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? __________

Solution:
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

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