Question

The mean incubation time for a type of fertilized egg kept at 100.6?°F is 21 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 hatches between 19 and 21 ?days? ?(c) What is the probability that a randomly selected fertilized egg takes over 25 days to? hatch? ?(a) The probability that a randomly selected fertilized egg hatches in less than 17 days is nothing. ?(Round to four decimal places as? needed.)

Answer 1

Given,

= 21, = 2

We convert this to standard normal as

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

a)

P( X < 17) = P( Z < 17 - 21 / 2)

= P( Z < -2 )

= 1 - P( Z < 2)

= 1 - 0.9772

= 0.0228

b)

P( 19 < X < 21) = P( X < 21) - P( X < 19)

= P( Z < 21 - 21 / 2) - P( Z < 19 - 21 / 2)

= P( Z < 0) - P( Z < -1)

= 0.5 - ( 1 - 0.8413)

= 0.3413

c)

P( X > 25) = P( Z > 25 - 21 / 2)

= P( Z > 2)

= 1 - P( Z < 2)

= 1 - 0.9772

= 0.0228