Company A designs and manufactures trains and planes and relies on large deals f

Question

Company A designs and manufactures trains and planes and relies on large deals from its customers for these high-cost products. This series of large contracts makes for a very variable revenue stream compared with the more even income it derives from long-term service contracts. The share of revenue from services dropped from 23% to 14% between 2007 and 2010 compared with the much higher figure of 51% for Company B in 2010. In 2011, an analyst predicts that Company A's service share will drop to 12% with a standard deviation of 44% in 2014 and that Company B's service share will increase to 53% with a standard deviation of 22%. Complete parts a) through c) below, assuming the forecast is accurate.

a) Find the probability that Company A's service share will be lower in 2014 than in 2010.

The probability that Company A's service share will be lower is ---

b) Find the probability that Company B's service share will be higher in 2014 than in 2010.

The probability that Company B's service share will be higher is ---

Explanation / Answer

a)

Assuming that each service share percentage can be modelled by a Normal random variable

Let X be the Company A's service share in 2014

Company A's service share in 2010 is 14%

Probability that Company A's service share will be lower in 2014 than in 2010 = P(X < 14)

= P[Z < (14 - 12) / 44] = P(Z < 0.0455) = 0.5181

b)

Let Y be the Company B's service share in 2014

Company B's service share in 2010 is 51%

Probability that Company B's service share will be higher in 2014 than in 2010 = P(X > 51)

= P[Z > (51-53) / 22] = P(Z > -0.0909) = 0.5362

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