Normal distribution (PROBI)

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2012-10-23 8:20 pm

A researcher reports that snakes will live an mean of 40 months when their diets are restricted and then enriched with vitamins. Assuming that the lifetimes of such snakes are normally distributed with a standard deviation of 6.3 months, find the probability that a given snake will live

(a) more than 32 months
(b) less than 28 months
(c) between 37 and 49 months

更新1:

myisland8132 : how to calculate the answer?? from P(Z > -1.2698) to 0.8979 if i dont want to get answer from table.. any formula??

回答 (1)

myisland8132

2012-10-23 9:12 pm

✔ 最佳答案

Let thelifetime of a snake is X

(a) P(X > 32)

= P(Z > (32 - 40)/6.3)

= P(Z > -1.2698)

= 0.8979

(b) P(X < 28)

= P(Z > (28 - 40)/6.3)

= P(Z < -1.9045)

= 0.028406

(c) P(37 <= X <= 49)

= P( (37 - 40)/6.3 <= Z <= (49 - 40)/6.3)

= P(-0.4762 <= Z <= 1.4286)

= 0.6065

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