The mean incubation time for a type of fertilized egg kept at 100.7 degrees F is

Question

The mean incubation time for a type of fertilized egg kept at 100.7 degrees 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 15 days is? b)The probability that a randomly selected fertilized egg takes over 23 days to hatch is? c) The probability that a randomly selected fertilized egg hatches between 17 and 19 days is? d) Would it be unusual for an egg to hatch in less than 16 days? Why?

Explanation / Answer

The mean incubation time for a type of fertilized egg kept at 100.7 degrees 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 15 days is?

Z=(15-19)/2 =-2

P( x <15) = p( z < -2) = 0.0228

b)The probability that a randomly selected fertilized egg takes over 23 days to hatch is?

Z=(23-19)/2 =4

P( x > 23) = p( z >2) = 0.0228

c) The probability that a randomly selected fertilized egg hatches between 17 and 19 days is?

Z=(17-19)/2 =-1

Z=(19-19)/2 =0

P( 17<x <19) = p(-1 < z <0)

P( z < 0) – P( z < -1)

=0.5 - 0.1587 = 0.3413

d) Would it be unusual for an egg to hatch in less than 16 days? Why?

Z=(16-19)/2 =-1.5

P( x <16) = p( z < -1.5) = 0.0668

It is not unusual for an egg to hatch in less than 16 days because P=0.0668 > 0.05.

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