Question

The 5200 chickens at colonel Thompson’s ranch have a mean wieght of 1850 g. With a standard deviation of 150g. Find the number of chickens weighing between 1750 and 1900g?

Please show the formula used BEFORE plugging in the actual numbers

Answer 1

Result P (1750<X<1900) 0.3779 Explanation Step 1: Sketch the curve. The probability that 1750 < X < 1000 is equal to the blue area under the curve. 0.0035 0.0030 0.0025 0.0020 0.0015 0.0010 0.0005 0.0000 1750 1900 0.0005 300 1400 500 1600 1700 180 900 2000 2100 2200 2300 2400 Step 2: Since μ = 1850 and σ = 150 we have: 1750-1850 X-μ 1900-1850 P(1750 < X < 1900 ) = P ( 1750-1850 < -μ<1000-1850)=P 150

Step 2: Since μ-1850 and σ-150 we have. 1750-1850 X-μ 1900-1850 (- 150 P(1750 < X < 1900 )-P(1750-1850 < X-μ<1000-1850)-P · , 174-180-0.67 and-T50- 101150850 = 0.33 we have: z-p 151 F) ( 1750 < X < 1900 ) = P (-0.67 < Z < 0.33 ) Step 3: Use the standard normal table to conclude that: P (-0.67 < Z < 0.33 ) 0.3779