Question

Big chickens: According to a poultry industry news website, the weights of broilers (commercially raised chickens) are approximately normally distributed with mean

1521

grams and standard deviation 166 grams. Use the Cumulative Normal Distribution Table to answer the following.

(a) What proportion of broilers weigh between

1185 and 1283 grams?

(b) What is the probability that a randomly selected broiler weighs more than 1650 grams?

(c) Is it unusual for a broiler to weigh more than

1710 grams? Round the answers to at least four decimal places.

Answer 1

Solution :

Given that ,

mean = = 1521

standard deviation = = 166

a) P( 1185 < x < 1283) = P[(1185 - 1521)/ 166) < (x - ) /  < (1283 - 1521) / 166 ) ]

= P(-2.02 < z < -1.43)

= P(z < -1.43) - P(z < -2.02)

Using z table,

= 0.0764 - 0.0217

= 0.0547

b) P(x > 1650) = 1 - p( x< 1650 )

=1- p P[(x - ) / < (1650 - 1521) / 166]

=1- P(z < 0.78)

Using z table,

= 1 - 0.7823

= 0.2177

c) P(x > 1710) = 1 - p( x< 1710 )

=1- p P[(x - ) / < (1710 - 1521) / 166]

=1- P(z < 1.14)

Using z table,

= 1 - 0.8729

= 0.1271

No, Is it not unusual for a broiler to weigh more than 1710 gram because probability is more than 5%