The mean incubation time for a type of fertilized egg kept at 100.5 degree F is

Question

The mean incubation time for a type of fertilized egg kept at 100.5 degree F is 19 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 17 days? (b) What is the probability that a randomly selected fertilized egg takes over 21 days to hatch? What is the probability that a randomly selected fertilized egg hatches between 15 and 19 days? (d) Would it be unusual for an egg to hatch in less than 13days? Why? (a) The probability that a randomly selected fertilized egg hatches in less than 17 days is

Explanation / Answer

a) Mean = 19 days

Standard deviation = 2 days

a) P(less than 17 days) = P(X<17)

= P(Z < (17- mean)/standard deviation)

= P(Z < (17-19)/2)

= P(Z<-1) = 0.1587

b) P(X>21)

= 1 - P(X<21)

= 1 - P(Z < (21-19)/2)

= 1 - P(Z <1)

= 1 - 0.8413

= 0.1587

c) P(15 < X < 19)

= P(X<19) - P(X<15)

= 0.5 - P(Z<-2)

= 0.5 - 0.0228

= 0.4772

d) P(X<13) = P(Z < (13-19)/2)

= P(Z < -3)

= 0.0013 <0.05

So, it would be unusual for an egg to hatch in less than 13 days

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