Question

The mean lifespan of the insect is 144 days and the standard deviation of its lifespan is 16 days. Find the probability that the next insect studied lives:
a) Less than 140 days
b)More than 156 days

Answer 1

a)

From central Limit Theorem $P(x<140)=P(\frac{x-144}{16} < \frac{140-144}{16}) = P(\frac{x-144}{16} < -0.25)$ is equivalent to $F(z<-0.25)$ where $z \sim N(0,1)$

From table F(-0.25)=0.4013

Ans 0.4013

b)

From central Limit Theorem $P(x>156)=P(\frac{x-144}{16} > \frac{156-144}{16}) = P(\frac{x-144}{16} > 0.75)$ is equivalent to $F(z>0.75)$ where $z \sim N(0,1)$

$F(z>0.75)=1 - F(z<0.75)=1 - .7734 = 0.2266$

Ans 0.2266