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Vandelay Industries has determined the probability of shipping wedding invitation envelopes witl contaminateçglue on the envelope flap is .4. Vandelay has experienced losses from $1,000 to $10,000. The expected loss per customer is $3,200 with a standard deviation of $56.57, and coefficient of variation of 1.41 . Which of the following is a random variable?

a.The 4 probability
b.A $10,000 loss
c. The $56.57 standard deviation
d.A 1.41 coefficient of variation

User Breeno
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1 Answer

5 votes

Final answer:

The amount of loss is considered a random variable because it can vary due to random factors such as contamination incidence and customer reactions.

Option b, a $10,000 loss, fits the definition of a random variable as it represents a potential outcome from shipping contaminated envelopes.

Step-by-step explanation:

The question relates to the concept of a random variable in probability and statistics. A random variable is a numerical quantity whose value depends on the outcome of a random event. In the context of Vandelay Industries, the probability of shipping wedding invitation envelopes with contaminated glue on the envelope flap is a fixed value of 0.4 and hence is not a random variable.

Therefore, option a is not correct. The possible loss from shipping these envelopes, which can range from $1,000 to $10,000, is unpredictable and depends on many random factors, such as the occurrence of contamination, customer complaints, and loss claims.

Thus, the amount of loss can vary and fits the definition of a random variable. Consequently, option b which mentions a $10,000 loss, would be a random variable as it represents one possible outcome of the aforementioned random event. The standard deviation ($56.57) and the coefficient of variation (1.41) are measurements describing the distribution of the random variable but are not random variables themselves.

User Christofer Weber
by
8.1k points
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