Question

Question 4 6 pts The chickens at Colonel Thompson's Ranch have a mean weight of 1850 g, with a standard deviation of 150 g. The weights of the chickens are closely approximated by a normal curve. Find the probability of all chickens having weights in the following ranges. a) Between 1750 and 1900 g (Round to 4 decimal places) (Round to 4 decimal places) b) More than 2100 g or less than 1550g (Round to 1 decimal place) c) Find the smallest weight for the top 5% of the chickens, 6 pts D Question 5

Answer 1

Solution:- Given that mean = 1850, sd = 150

a) P(1750 < X < 1900) = P((1700-1850)/150 < (X-mean)/sd < (1900-1850)/150)
= P(-1 < Z < 0.3333)
= P(Z < 0.3333) − P(Z < −1)
= 0.6293 - 0.1587
= 0.4706

b)P(X > 2100) + P(X < 1550) = 0.0475+0.0228 = 0.0703

P(X > 2100) = P(Z > (2100-1850)/150))
= P(Z > 1.6667)
= 1 − P(Z < 1.6667)
= 1 − 0.9525
= 0.0475
  
P(X < 1550) = P(Z < −2) = 1 − P(Z < 2) = 1 − 0.9772 = 0.0228

c) for Z = 1.645

X = mean + Z*sd = 1850 + 1.645*150 = 2096.75 = 2096.8