The mean incubation time for a type of fertilized egg kept at 100.3\'F is 22 day

Question

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 2 days. (a) What is the probability that a randomly selected fertilized egg hatches in less than 18 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 26 days to hatch? (a) The probability that a randomly selected fertilized egg hatches in less than 18 days is (Round to four decimal places as needed) (b) The probability that a randomly selected ferilized egg hatches between 20 and 22 days is (Round to four decimal places as needed)

Explanation / Answer

Solution:- Given that mean = 22 days , Sd = 2 days

a) P(X < 18) = P(Z < (x - ?/?)
= P(Z < (18 - 22)/2)
= P(Z < -4/2)
= P(Z < -2)
= 0.0228

b) P(20 < X < 22) = P((20 - 22)/2 < Z < (22 - 22)/2)
= P(-1 < Z < 0)
= 0.3413

c) P(X > 26) = P(Z > 26 - 22)/2)
= P(Z > 2)
= 0.0228

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