The mean incubation t standard deviation of 2 days time for a type of fertilized

Question

The mean incubation t standard deviation of 2 days time for a type of fertilized egg kept at 100 1'F is 22 days. Suppose that the incubation times are approximately normally distributed with a (a) What is the probability that a randomly selected fertilized egg hatches in less than 20 days? (b) What is the probability that a randomly selected fertilized egg hatches between 18 and 22 days? (c) What is the probability that a randomly selected fertilized egg takes over 24 days to hatch? (e) The probability that a randomly selected fertilized egg hatches in less than 20 days is Round to four decimal places as needed.)

Explanation / Answer

Solution:- Given that mean = 22 days and standard deviation 2 days

(a) The probability that a randomly selected fertilized egg hatches in less than 20 days is 0.1587

=> P(X < 20) = P((x-mean)/sd < (20-22)/2 )
= P(Z < -1)
= 0.1587

(b) The probability that a randomly selected fertilized egg hatches between 18 and 22 days is 0.4772

=> P(18 < x < 22) = P((18-22)/2 < Z < (22-22)/2)
= P(-2 < Z < 0)
= 0.4772

(c)The probability that a randomly selected fertilized egg take over 24 days is 0.1587
=> P(X > 24) = P(Z > (24-22)/2)
= P(Z > 1)
= 0.1587

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