The mean incubation time for a type of fertilized egg kept at 100.6 degree F is

Question

The mean incubation time for a type of fertilized egg kept at 100.6 degree F is 23 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 lees than 21 days? (b) What is the probability that a randomly selected fertilized egg hatches between 19 and 23 days? (c) What is the probability that a randomly selected fertilized egg takes over 26 days to hatch? (a) The probability that a randomly selected fertilized egg hatches in less than 21 days is .

Explanation / Answer

Mean ( u ) =23
Standard Deviation ( sd )=2
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
P(X < 21) = (21-23)/2
= -2/2= -1
= P ( Z <-1) From Standard Normal Table
= 0.1587                  
b.                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 19) = (19-23)/2
= -4/2 = -2
= P ( Z <-2) From Standard Normal Table
= 0.02275
P(X < 23) = (23-23)/2
= 0/2 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(19 < X < 23) = 0.5-0.02275 = 0.4772                  
c.
P(X > 25) = (25-23)/2
= 2/2 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587

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