Question

The mean incubation time for a type of fertilized egg kept at 100.9​°F is 21 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 19 ​days? ​(b) What is the probability that a randomly selected fertilized egg takes over 23 days to​ hatch? ​(c) What is the probability that a randomly selected fertilized egg hatches between 20 and 21 ​days? ​(d) Would it be unusual for an egg to hatch in less than 18 ​days? Why?

Answer 1

Explanation:

Given that the mean incubation time (say X) for a type of fertilized egg kept at 100.9​°F is 21 days.

X is N( 21,1)

a) the probability that a randomly selected fertilized egg hatches in less than 19 ​days

=
`P(X<19) = P(Z<(19-21)/(1) \\=P(Z<-2) \\=0.02275`

b) the probability that a randomly selected fertilized egg takes over 23 days to​ hatch

=P(X>26) = 0.000

(almost uncertain event)

c) the probability that a randomly selected fertilized egg hatches between 20 and 21 ​days

= F(21)-F(20) = 0.341345

d) Let us find prob P(X<18)

= 0.00135

Yes, unusual because probability is very less and near to 0