The mean incubation time for a type of fertilized egg kept a

The mean incubation time for a type of fertilized egg kept at 100.6F is 19 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day.

a.) What is the probability that a randomly selected fertilized egg hatches in less than 17 days?

b.) What is the probability that a randomly selected fertilized egg hatches between 18 and 19 days?

c.) What is the probability that a randomly selected fertilized egg takes over 21 days to hatch?

Solution

a)
Here x =17, mu=19 and sigma=1

z= (x -mu)/sigma=(17-19)/1= -2

Need to find , P(x<17)=P(z<-2)=0.0228(Ans.)

b)
Here x =18, mu=19 and sigma=1

z= (x -mu)/sigma=(18-19)/1= -1

Here x =19, mu=19 and sigma=1

z= (x -mu)/sigma=(19-19)/1= 0

Need to find , P(18<x<19)=P(-1<z<0)= ( 0.5 - 0.1587) = 0.3413 Answer

c)
Here x =21, mu=19 and sigma=1

z= (x -mu)/sigma=(21-19)/1= 2

Need to find , P(x>21)=P(z>2)=1 - .9772 = 0.0228(Ans.)