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A company producing orange juice buys all of its oranges from a large orange orchard. The amount of juice that can be squeezed from each of these oranges is a continuous variable that has a bell shaped curve probability density function, with a mean of 4.7 ounces and some unknown standard deviation. The company's production manager knows that the probability is 30.85% that a randomly selected orange will contain less than 4.5 ounces of juice. Also, the probability is 10.56% that a randomly selected orange will contain more than 5.2 ounces of juice. Answer the following questions by drawing a bell shaped curve centered at 4.7 and take advantage of the facts that the density curve is symmetrical with respect to its center and the area under the whole curve is 100% probability.
a. What is the probability that a randomly selected orange will contain between 4.5 and 5.2 ounces of juice?
b. What is the probability that a randomly selected orange will contain between 4.2 and 4.9 ounces of juice?
c. What is the probability that a randomly selected orange will contain at least 4.9 ounces of juice?
d. What is the probability that a randomly selected orange will contain no more than 4.9 ounces of juice?
e. What is the probability that a randomly selected orange will contain no more than 4.2 ounces of juice?
f. What is the probability that a randomly selected orange will contain more than 4.2 ounces of juice?
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