The mean incubation time for a type of fertilized egg kept a

The mean incubation time for a type of fertilized egg kept at 100.1 degree F is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day.

a. probability that a randomly selected egg hatches in less than 20 days

b. betwen 21 and 22 days

c. probability it takes over 24 days

Solution

a. probability that a randomly selected egg hatches in less than 20 days

P(X<20) = P((X-mean)/s <(20-22)/1)

=P(Z<-2) =0.0228 (from standard normal table)

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b. betwen 21 and 22 days

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

=P(-1<Z<0)

=0.3413 (from standard normal table)

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c. probability it takes over 24 days

P(X>24) = P(Z>(24-22)/1)

=P(Z>2) =0.0228 (from standard normal table)