The mean incubation time for a type of fertilized egg kept at 100.9°F is 22 days

Question

The mean incubation time for a type of fertilized egg kept at 100.9°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 20 days? (b) What is the probability that a randomly selected fertilized egg hatches between 21 and 22 days? (c) What is the probability that a randomly selected fertilized egg takes over 24 days to hatch? (a) The probability that a randomly selected fertlized egg hatches in less than 20 days is Round to four decimal places as needed.) (b) The probability that a randomly selected fertilized egg hatches between 21 and 22 days is (Round to four decimal places as needed.) (c) The probability that a randomly selected fertilized egg takes over 24 days to hatch is (Round to four decimal places as needed.)

Explanation / Answer

Mean = 22 days

Standard deviation = 1 day

a) P(a randomly selected fertlized egg hatches in less than 20 days) = P(X < 20)

= P(Z < (20-22)/1)

= P(Z < -2)

= 0.0228

b) P(a randomly selected fertlized egg hatches between 21 and 22 days) = P(X < 22) - P(X < 21)

= 0.5 - P(Z < (21-22)/1)

= 0.5 - P(Z < -1)

= 0.5 - 0.1587

= 0.3413

c) P(a randomly selected fertlized egg takes over 24 days to hatch) = P(X > 24)

= 1 - P(X < 24)

= 1 - P(Z < (24 -22)/1)

= 1 - P(Z < 2)

= 1 - 0.9772

= 0.0228

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