The mean incubation time for a type of fertilized egg kept at 100.7 degree F is

Question

The mean incubation time for a type of fertilized egg kept at 100.7 degree F is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. What is the probability that a randomly selected fertilized egg hatches in less than 21 days? What is the probability that a randomly selected fertilized egg hatches between 20 and 22 days? What is the probability that a randomly selected fertilized egg takes over 23 days to hatch? The probability that a randomly selected fertilized egg hatches in less than 21 days is ___. (Round to four decimal places as needed.)

Explanation / Answer

a) There is a probability 0.6827 fot the observation to be within 1 standard deviation

21 is 1 standard deviation away from mean

P(X < 21) = 0.6827/2 + 0.5 = 0.8414

b)22 is 2 standard deviation from mean

Probability of an observation to be within 2 standard deviations = 0.9545

So, P(20 < X < 22) = 0.9545/2 = 0.4773

c) 23 is 3 standard deviation from mean

P(X > 23) = 1 - P(X <23)

= 1 - (0.5 + 0.9973/2)

= 0.0014

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