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24 January, 14:59

The mean incubation time for a type of fertilized egg kept at 100.2100.2â°f is 2323 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 11 dayday. â (a) what is the probability that a randomly selected fertilized egg hatches in less than 2121 âdays? â (b) what is the probability that a randomly selected fertilized egg hatches between 2222 and 2323 âdays? â (c) what is the probability that a randomly selected fertilized egg takes over 2525 days toâ hatch?

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  1. 24 January, 15:10
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    To solve this problem, what we have to do is to calculate for the z scores of each condition then find the probability using the standard normal probability tables for z.

    The formula for z score is:

    z = (x - u) / s

    where,

    x = sample value

    u = sample mean = 23 days

    s = standard deviation = 1 day

    A. P when x < 21 days

    z = (21 - 23) / 1

    z = - 2

    Using the table,

    P = 0.0228

    Therefore there is a 2.28% probability that the hatching period is less than 21 days.

    B. P when 23 ≥ x ≥ 22

    z (x=22) = (22 - 23) / 1 = - 1

    P (z=-1) = 0.1587

    z (x=23) = (23 - 23) / 1 = 0

    P (z=0) = 0.5

    P = 0.5 - 0.1587 = 0.3413

    Therefore there is a 34.13% probability that the hatching period is between 22 and 23 days.

    C. P when x > 25

    z = (25 - 23) / 1

    z = 2

    P = 0.9772

    This is not yet the answer since this probability refers to the left of z. Therefore the correct probability is:

    P true = 1 - 0.9772

    P true = 0.0228

    Therefore there is a 2.28% probability that the hatching period is more than 25 days.
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