The chickens at Colonel​ Thompson's Ranch have a mean weight of 1700 ​g, with a standard deviation of 200 g. The weights of the chickens are closely approximated by a normal curve. Find the percent of all chickens having weights more than 1560 g.

Accepted Solution

Answer:75.8%Step-by-step explanation:Mean weight of chickens = u = 1700 gStandard deviation = [tex]\sigma[/tex] = 200gWe need to calculate the percentage of chickens having weight more than 1560 gSo, x = 1560 gSince the weights can be approximated by normal distribution, we can use concept of z-score to solve this problem.First we need to convert the given weight to z score. The formula for z score is:[tex]z=\frac{x-u}{\sigma}[/tex]Using the values, we get:[tex]z=\frac{1560-1700}{200} \\\\ z = -0.7[/tex]So now we have to calculate what percentage of values lie above the z score of -0.7. Using the z-table or z-calculator we get:P(z > -0.7) = 0.758This means 0.758 or 75.8% of the values are above z score of -0.7. In context of our question we can write:75.8% of the chickens will have weight more than 1560 g