Question

1. The incubation time for Rhode Island Red chicks is normally distributed with a mean of 21 days and standard deviation of 1 day. If 1000 eggs are being incubated, how many chicks do we expect will hatch: (In this problem consider a single day or succession of days as a continuous interval of time)
   1. In 19 to 23 days
   2. In 20 to 22 days
   3. In 21 days or fewer
   4. In 18 to 24 days

Answer 1

Solution :

Given that ,

mean = = 21 days

standard deviation = = 1 day

n = 1000

a) P( 19 < x < 23) = P[(19 - 21 ) / 1) < (x - ) /  < (23 - 21) / 1 ) ]

= P( -2.00 < z < 2.00)

= P(z < 2.00 ) - P(z < -2.00)

Using z table,

= 0.9772 - 0.0228

= 0.9544

1000 * 0.9544 = 954.4

954 chicks.

b) P( 20 < x < 22) = P[(20 - 21 ) / 1) < (x - ) /  < (22 - 21) / 1 ) ]

= P( -1.00 < z < 1.00)

= P(z < 1.00 ) - P(z < -1.00)

Using z table,

= 0.8413 - 0.1587

= 0.6826

1000 * 0.6826 = 682.6

683 chicks.

c) P(x 21 )

= P[(x - ) / (21 - 21) / 1 ]

= P(z 0.00)

Using z table,

= 0.5

1000 * 0.5 = 500 chicks.

d) P( 18 < x < 24) = P[(18 - 21 ) / 1) < (x - ) /  < (24 - 21) / 1 ) ]

= P( -3.00 < z < 3.00)

= P(z < 3.00 ) - P(z < -3.00)

Using z table,

= 0.9987 - 0.0013

= 0.9974

1000 * 0.9974 = 997.4

997 chicks.