question 14 The mean incubation time for a type of fertilized egg kept at 100.6°
ID: 3183469 • Letter: Q
Question
question 14
The mean incubation time for a type of fertilized egg kept at 100.6°F is 23 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 11 day.
(a) What is the probability that a randomly selected fertilized egg hatches in less than 22 days?
(b) What is the probability that a randomly selected fertilized egg takes over 24 days to hatch?
(c) What is the probability that a randomly selected fertilized egg hatches between 21 and 23 days?
(d) Would it be unusual for an egg to hatch in less than 21.5 days? Why?
The probability of this event is ___so it would/would not be unusual because the probability is greater/less than 0.05.
Explanation / Answer
Given = 23, = 11
Z = (x-)/, where x is raw score
a) P(X<22) = P[Z<(23-22)/11] = P (Z<0.09)
= 0.4641
b) P ( X>24 )=P ( X/>2423/11)
= P ( Z>0.09 ) = 10.5359=0.4641
c) P ( 21<X<23 )=P ( 2123/11<X/<2323/11)
= =P ( 0.18<Z<0 ) = 0.0714
d) P ( X<21.5 )=P (X/<21.523/11)
=P (Z<0.14) = 0.444
The probability of this event is 0.444 so it would be unusual because the probability is greater than 0.05.
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