Question

My Notes The incubation time for a breed of chicks is normally distributed with a mean of 21 days and standard deviation of approximately 2 days. Look at the four 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, et us agree to think of a single day or a succession of as a continuous interval of time. Assume all eggs eventually hatch.) Area Under a Normal Curve 34% 34% 13.5% 2.39% (a) in 17 to 25 days X chicks (b) in 19 to 23 days X chicks (c) in 21 days or fewer chicks (d) in 15 to 27 days 99 chicks

Answer 1

X=The incubation time for Rhode Island Red chicks

$X~N(\mu =21,\sigma =2)$

a)P[17<X<25]

$P(\frac{17-21}{2}<\frac{x-\mu}{\sigma }<\frac{25-21}{2})$

=P[-2<Z<2]

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

=0.9772-.0228..........................by using normal probability table.

=0.945

Therefore, 1000*0.9545=955

955 chicks

b)P[19<X<23]

$P(\frac{19-21}{2}<\frac{x-\mu}{\sigma }<\frac{23-21}{2})$

=P[-1<Z<1]

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

=0.8413-.1587..........................by using normal probability table.

=0.6827

Therefore, 1000*0.6827=682.69

683 chicks