The maximum patent life for a new drug is 17 years. Subtracting the length of ti

Question

The maximum patent life for a new drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life of the drug—that is, the length of time that a company has to recover research and development costs and make a profit. Suppose the distribution of the lengths of patent life for new drugs is as shown here.

0.03 0.01

A) Find the expected number of years of patent life for a new drug.

B) Find the standard deviation of x. (Round your answer to four decimal places.)

C) Find the probability that x falls into the interval ± 2.

Years, x 3 4 5 6 7 8 9 10 11 12 13 p(x) 0.02    0.05   0.07   0.10   0.14 0.23 0.16   0.12 0.07   

0.03 0.01

Explanation / Answer

Solution:-

A) x = 0.02*3 + 0.05*4 + 0.07*5 + 0.1*6 + 0.14*7 + 0.23*8 + 0.16*9 + 0.12*10 + 0.07*11 + 0.03*12 + 0.01*13 = 7.93

B)  x = sqrt(0.02*(3 - 7.93)^2 + 0.05*(4 - 7.93)^2 + 0.07*(5 - 7.93)^2 + 0.1*(6 - 7.93)^2 + 0.14*(7 - 7.93)^2 + 0.23*(8 - 7.93)^2 + 0.16*(9 - 7.93)^2 + 0.12*(10 - 7.93)^2 + 0.07*(11 - 7.93)^2 + 0.03*(12 - 7.93)^2 + 0.01*(13 - 7.93)^2)

  x = 2.1131

C) P(7.93 - 2*2.1131 < X < 7.93 + 2*2.1131) = P(3.7038 < X < 12.1562)

=  P((3.7038 - 7.93)/2.1131 < Z < (12.27 + 7.93)/2.1131)

= (-2 < Z < 9.5594)

=  0.9772

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