Question

The mean incubation time for a type of fertilized egg kept at a certain temperature is 19 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. Complete parts​ (a) through​ (e) below.

(a) Draw a normal model that describes egg incubation times of these fertilized eggs.

(b)Find and interpret the probability that a randomly selected fertilized egg hatches in less than

17 days.

(c) Find and interpret the probability that a randomly selected fertilized egg takes over 21 days to hatch.

(d) Find and interpret the probability that a randomly selected fertilized egg hatches between

15 and 19 days.

(e) Would it be unusual for an egg to hatch in less than 13 days? Why?

Answer 1

mean incubation time for a type of fertilized egg kept at a certain temperature = 19 days

standard deviation incubation time for a type of fertilized egg kept at a certain temperature = 1 day

Let X denotes incubation time for a type of fertilized egg kept at a certain temperature

mean_X = 19

SD_X = 1

a) Normal model = Z = ( X - mean_X )/SD_X

Z = ( X - 19 )/1 = X - 19

b) Probability that a randomly selected fertilized egg hatches in less than 17 days = P[ X < 17 ]

P[ X < 17 ] = P[ ( X - 19 ) < ( 17 - 19 ) ] = P[ Z < -2 ] = 0.0228

Intercept = -2

Probability = 0.028

c) Probability that a randomly selected fertilized egg hatches in more than 21 days = P[ X > 21 ]

P[ X > 21 ] = P[ ( X - 19 ) > ( 21 - 19 ) ] = P[ Z > 2 ] = 0.0228

Intercept = 2

Probability = 0.028

d) Probability that a randomly selected fertilized egg hatches between 15 and 19 days = P[ 15 < X < 19 ]

P[ 15 < X < 19 ] = P[ ( 15 - 19 ) < ( X - 19 ) < ( 19 - 19 ) ] = P[ -4 < Z < 0 ] = 0.5

Intercept = 0

Probability = 0.5

e) For that we need to calculate P[ X < 13 ]

P[ X < 13 ] = P[ ( X - 19 ) < ( 13 - 19 ) ] = P[ Z < -6 ] = 0

Yes, since the probability is zero. Therefore, it will be unusual for an egg to hatch in less than 13 days