The incubation time for Rhode Island Red chicks is normally distributed with a m

Question

The incubation time for Rhode Island Red chicks is normally distributed with a mean of 20 days and standard deviation of approximately 1 day. 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.) Area Under a Normal Curve 2.3 13.5% | 34% | 34% | 13.5% 2.35% 68% 95% 99.7% (a) in 18 to 22 days 13.5 X chicks (b) in 19 to 21 days chicks (c) in 20 days or fewer chicks (d) in 17 to 23 days chicks

Explanation / Answer

Solution :

Given that mean ? = 20 , standard deviation ? = 1

(a) in 18 to 22 days

P(18 < x < 22) = P((x - ?)/? < Z < (x - ?)/?)

= P((18 - 20)/1 < Z < (22 - 20)/1)

= P(-2 < Z < 2)

= 95% out of 1000

= 950 chicks

(b) in 19 to 21 days

P(19 < Z < 21) = P((19 - 20)/1 < Z < (21 - 20)/1)

= P(-1 < Z < 1)

= 68% out of 1000

= 680 chicks

(c) in 20 days or fewer

P(x < 20) = P(Z < (20 - 20)/1)

= P(Z < 0)

= 0.50

= 0.50*1000

= 500 chicks

(d) in 17 to 23 days

P(17 < x < 23) = P((17 - 20)/1 < Z < (23 - 20)/1)

= P(-3 < Z < 3)

= 99.7% out of 1000

= 997 chicks

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.