The mean incubation time for a type of fertilized egg kept at 100.3 degree F is

Question

The mean incubation time for a type of fertilized egg kept at 100.3 degree F is 21 days. Suppose that the incubation times are app distributed with a standard deviation of 1 day. (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 takes over 22 days to hatch? (c) What is the probability that a randomly selected fertilized egg hatches between 19 and 21 days? (d) Would it be unusual for an egg to hatch in less than 18 days? Why? (a) The probability that a randomly selected fertilized egg hatches in less than 20 days is __. (Round to four decimal places as needed.) (b) The probability that a randomly selected fertilized egg takes over 22 days to hatch is __. (Round to four decimal places as needed.) (c) The probability that a randomly selected fertilized egg hatches between 19 and 21 days is __. (Round to four decimal places as needed.) (d) Would it be unusual for an egg to hatch in less than 18 days? Why? The probability of this event is __, so it _____ be unusual because the probability is _____ than 0.05. (Round to four decimal places as needed.)

Explanation / Answer

a) P(X<20)

P(Z<(22-21)/1)

= P(Z<-1)

= 0.1587

So, answer is 0.1587

b) P(X>22)

P(Z>(22-21)/1)

= P(Z>1)

= 0.1587

So, answer is 0.1587

c) P(19<x<21)

= P(-2<z<0)

= 0.4773

So, answer is 0.4773

d) P(X<18)

= P(Z<(18-21)/1)

= P(Z<-3)

= 0.0014

So, probability of this event is 0.0014, so it wil be unusual because the probability is less than 0.05

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