1.An orange juice producer buys all his oranges from a large orange grove. The a
ID: 3292046 • Letter: 1
Question
1.An orange juice producer buys all his oranges from a large orange grove. The amount of juice squeezed from each of these oranges is approximately distributed with a mean of 4.70 ounces and a standard deviation of 0.40 ounce.
a.What is the probability that a randomly selected orange will contain between 4.60 and 5.00 ounces?
b.77% of the oranges will contain less than how many ounces of juices?
c.Suppose that a sample of 25 oranges is selected. What is the probability that the sample mean will be at least 4.60 ounces?
Explanation / Answer
a)
P(4.6 < X < 5) = P(X < 5) - P(X < 4.6)
= P(Z < 5 -4.7/0.4) - P(Z < 4.6-4.7/0.4)
= P(Z < 0.75) - P(Z < -0.25)
= 0.7734 - 0.4013
= 0.3721
b)
P(X <x) = 0.77
=>
x - 4.7/0.4 = invnorm(0.77)
x = 4.9956
c)
P(X >=4.6) = P(Z > 4.6 - 4.7/0.4/sqrt(25))
= P(Z > -1.25)
= 0.8944
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