Question

if the mean lifespan of an insect is 144 days and the standard deviation of its lifespan is 16 days find the probability that the next insect studied lives less than 140 days

Answer 1

Answer on Question #40985, Math, Statistics and Probability

Question:

if the mean lifespan of an insect is 144 days and the standard deviation of its lifespan is 16 days find the probability that the next insect studied lives less than 140 days

Slution:

We have normal distribution with mean 144 and standard deviation – 16:

$$m = 144$$ $$\sigma_1 = 16$$

And we need to know:

$$P(x < 140)$$

Or we can write it as $P(x < 144 - 0.25 * 16)$ and find value of this probability using the table

http://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf

for $z = -0.25$

So, probability equals

$$P(x < 140) = P(x < 144 - 0.25 * 16) = P(z = -0.25) = 0.40129.$$

Answer: 0.40129.