Question

The mean incubation time for a type of fertilized egg kept at 100.8​°F is 21 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days. ​(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 hatches between 17 and 21 ​days? ​(c) What is the probability that a randomly selected fertilized egg takes over 23 days to​ hatch?

Answer 1

1)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	21
std deviation   =σ=	2.0000

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

probability =

P(X<19)

=

P(Z<-1)=

0.1587

2)

probability that a randomly selected fertilized egg hatches between 17 and 21 ​days:

probability =

P(17<X<21)

=

P(-2<Z<0)=

0.5-0.0228=

0.4772

3)

  probability that a randomly selected fertilized egg takes over 23 days to​ hatch:

probability =

P(X>23)

=

P(Z>1)=

1-P(Z<1)=

1-0.8413=

0.1587