(a) Loraine Corporation is planning to market a new makeup product. According to the analysis made by the financial department of the company, it will earn an annual profit of $4.5 million if this product has high sales, an annual profit of $1.2 million if the sales are mediocre, and it will lose $2.3 million a year if the sales are low. The probabilities of these three scenarios are 0.32, 0.51 and 0.17 respectively. Let x be the profits (in millions of dollars) earned per annum by the company from this product. Write the probability distribution of x. ii. Calculate the mean and standard deviations of x.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 5EA
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Question 1
(a) Loraine Corporation is planning to market a new makeup product. According to the
analysis made by the financial department of the company, it will earn an annual profit
of $4.5 million if this product has high sales, an annual profit of $1.2 million if the sales
are mediocre, and it will lose $2.3 million a year if the sales are low. The probabilities
of these three scenarios are 0.32, 0.51 and 0.17 respectively.
i.
Let x be the profits (in millions of dollars) earned per annum by the company
from this product. Write the probability distribution of x.
ii.
Calculate the mean and standard deviations of x.
Transcribed Image Text:Question 1 (a) Loraine Corporation is planning to market a new makeup product. According to the analysis made by the financial department of the company, it will earn an annual profit of $4.5 million if this product has high sales, an annual profit of $1.2 million if the sales are mediocre, and it will lose $2.3 million a year if the sales are low. The probabilities of these three scenarios are 0.32, 0.51 and 0.17 respectively. i. Let x be the profits (in millions of dollars) earned per annum by the company from this product. Write the probability distribution of x. ii. Calculate the mean and standard deviations of x.
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