The mean incubation time for a type of fertilized egg kept at 100.8100.8°F is 19

Question

The mean incubation time for a type of fertilized egg kept at 100.8100.8°F is 1919 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 22 daysdays. (a) What is the probability that a randomly selected fertilized egg hatches in less than 1515 days? (b) What is the probability that a randomly selected fertilized egg takes over 2323 days to hatch? (c) What is the probability that a randomly selected fertilized egg hatches between 1717 and 1919 days? (d) Would it be unusual for an egg to hatch in less than 1313 days? Why?

Explanation / Answer

(a)For X=15, z=(x-mu)/sigma

=(15-19)/22

=-0.36

P(X<15)=P(z<-0.36)=0.3594

(b) For X=23, z=(x-mu)/sigma

=(23-19)/22

=0.18

P(X>23)=P(z>0.18)=1-0.5714=0.4286

(c)For X=17, z=(17-19)/22

=-0.9

For X=19, z=(19-19)/22=0

P(17<X<19)=P(X<19)-P(X<17)

=P(z<0)-P(z<-0.9)

=0.5-01841=0.3159

d)For X=13, Z=(13-19)/22=-0.27

P(X<13)=P(z<-0.27)=0.3936

Yes,it is unusual for an egg to hatch in less than 1313 days as P(X<13)=0.3936 is less than 0.5.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.