Question

Big chickens: According to a poultry industry news website, the weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1358 grams and standard deviation 161 grams.

Is it unusual for a boiler to weigh more than 1550 grams?

Answer 1

Answer: Yes , it is unusual for a boiler to weigh more than 1550 grams .

Explanation:

Given : Big chickens: According to a poultry industry news website, the weights of broilers (commercially raised chickens) are approximately normally distributed with mean
`(\mu)` 1358 grams and standard deviation
`(\sigma)` 161 grams.

When the probability that broiler weigh more than 1550 grams < 0.5 , then is unusual otherwise not.

Let x denotes the weight of broiler, then the probability that broiler weigh more than 1550 grams :-

`P(x>1550)=1-P(x\leq1550)\\\\=1-P((x-\mu)/(\sigma)\leq(1550-1358)/(161))\\\\\approx 1-P(z\leq1.19)\ \ [\because\ z=(x-\mu)/(\sigma)]\\\\=\\\\=1-0.8830\ \ [\text{By using z-table}]\\\\=0.117`

Since 0.117<0.5

Therefore, it is unusual for a boiler to weigh more than 1550 grams .