A professor pays 25 cents for each error made in lecture tothe student who point

Question

A professor pays 25 cents for each error made in lecture tothe student who points out the error. In a career of n years filled with errors, the total amount indollars paid by a professor can be approximated by a Gaussian random variable Xn with mean 40nand variance 100n. (a) Determine the probability that X20 exceeds1000. (b) How many years n must the professor teach in order that [> 1000] > 0.99 n P X ? A professor pays 25 cents for each error made in lecture tothe student who points out the error. In a career of n years filled with errors, the total amount indollars paid by a professor can be approximated by a Gaussian random variable Xn with mean 40nand variance 100n. (a) Determine the probability that X20 exceeds1000. (b) How many years n must the professor teach in order that [> 1000] > 0.99 n P X ?

Explanation / Answer

From the problem X20 follows a normal distributionwith mean = 40*20 = 800 and = 100*20 = 2000

a)      P(X20 > 1000)= P(z > (1000-800)/2000 )

= P( (z> 0.1) = 46.01%

               

b)      Given that P(xn >1000 ) > 0.99

ð P( z > (1000 -40n)/100n ) > 0.99

ð (1000 -40n)/100n ) < 2.3263

ð . n > 3.667 years

Hope that helps your. Feel free to ask for clarifications.

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