Question

# The mean incubation time for a type of fertilized egg kept at 100.3?°F is 22 days....

The mean incubation time for a type of fertilized egg kept at 100.3?°F is 22 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 21 days?

?(b) What is the probability that a randomly selected fertilized egg hatches between 20 and 22 days?

?(c) What is the probability that a randomly selected fertilized egg takes over 23 days to? hatch?

Solution:

Given that, = 22 days = 1 day

a ) p ( x  < 21)

= p ( x - / ) < ( 21 - 22 / 1 )

= p ( z < - 1 / 1 )

= p ( z < - 1)

Using z table

= 0.1587

Probability = 0.1587

b ) p (20 < x  < 22)

= p ( 20 - 22 / 1 ) < ( x - / ) < ( 22 - 22 / 1 )

= p ( - 2 / 1 < z < 0 / 1 )

= p ( 0 < z < - 2 )

Using z table

= 0.5000 - 0.0228

= 0.4772

Probability = 0.4772

c ) p ( x  < 23)

= p ( x - / ) < ( 23 - 22 / 1 )

= p ( z < 1 / 1 )

= p ( z < 1 )

Using z table

= 0.8413

Probability = 0.8413