A research scientist reports that mice will live an average of 40 months when th

Question

A research scientist reports that mice will live an average of 40 months when their diets are sharply re- stricted and then enriched with vitamins and proteins. Assuming that the lifetimes of such mice are normally distributed with a standard deviation of 6.3 months, find the probability that a given mouse will live
(a) more than 32 months; (b) less than 28 months;
(c) between 37 and 49 months.

Explanation / Answer

(a) z=(32-40)/6.3=-1.27;P(X>32)=P(Z>-1.27)=1-0.1020=0.8980. (b) z = (28 - 40)/6.3 = -1.90, P(X < 28) = P(Z < -1.90) = 0.0287. (c) z1 = (37 - 40)/6.3 = -0.48, z2 = (49 - 40)/6.3 = 1.43; So, P (37

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