Question

The incubation time for a breed of chicks is normally distributed with a mean of 22 days and standard deviation of approximately 2 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.) (a) in 18 to 26 days chicks (b) in 20 to 24 days chicks (c) in 22 days or fewer chicks (d) in 16 to 28 days chicks

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	22
std deviation   =σ=	2.0000

hence P( 18 to 26 days )

probability =

P(18<X<26)

=

P(-2<Z<2)=

0.9772-0.0228=

0.9544

hence expected number =np=1000*0.9544=954.4 ~ 954

b)

probability =

P(20<X<24)

=

P(-1<Z<1)=

0.8413-0.1587=

0.6826

hence expected number =np=1000*0.6826=682.6 ~ 683

c)

probability =

P(X<22)

=

P(Z<0)=

0.5000

expected number =np=1000*0.5=500

d)

probability =

P(16<X<28)

=

P(-3<Z<3)=

0.9987-0.0013=

0.9974

expected number =np=1000*0.9974=997.4~ 997