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
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