Question

The mean incubation time for a type of fertilized egg kept at 100.6F 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 17 days?

(b) What is the probability that a randomly selected fertilized egg takes over 21 days to hatch?

(c) What is the probability that a randomly selected fertilized egg hatches between 15 and 19 days?

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

Answer 1

Given,

= 19 , ​​​​​​ = 2

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

a)

P(X < 17) = P(Z < ( 17 - 19) / 2 )

= P(Z < -1)

= 0.1587

b)

P(X > 21) = P(Z > ( 21 - 19) / 2)

= P(Z > 1)

= 0.1587

c)

P(15 < X < 19) = P(X < 19) - P(X < 15)

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

= P(Z < 0) - P(Z < -2)

= 0.5 - 0.0228

= 0.4772

d)

P(X < 16) = P(Z < ( 16 - 19) / 2 )

= P(Z < -1.5)

= 0.0668

Since this probability is greater than 0.05, it would not unusual for an egg to hatch in less than 16 days.