The mean incubation time for a type of fertilized egg kept at 100.4°F is 19 days

ID: 3010785 • Letter: T

Question

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

100.4°F

days. Suppose that the incubation times are approximately normally distributed with a standard deviation of

day.

What is the probability that a randomly selected fertilized egg hatches in less than

days?

(b) What is the probability that a randomly selected fertilized egg takes over

days to hatch?

(c) What is the probability that a randomly selected fertilized egg hatches between

and

days?

(d) Would it be unusual for an egg to hatch in less than

17.5

days? Why?

Here z score = (Given score - mean)/Deviation

So for part (a) z score = (17 - 19)/1 =-2

that is equivalent to P(Z<-2) = 0.023

that is required probability.

This is the answer of part (a)

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Again when given score is 21, then using same formula

Z = 21-19/1=2

so required probability P (Z<21) = 0.9772 = 0.98

This is the answer of part (b)

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Now when given score is 18, then

z = (18-19)/1=-1

so P( between 18 and 19) = P(-1<Z <0 ) = 0.5 - P(Z<-1) = 0.3413

This is the answer to part (c)

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Yes, it would be unusual for an egg to hatch in less than 17.5 days because then its probability is almost be 0.0,,,,,,

(as shown in part (a) also), that is neglegible.

This is the answer of part (d)

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