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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