Answer:
(a) 0.0329
(b) 0.3502
(c) It is not unusual for a broiler to weigh more than 1710 grams.
Step-by-step explanation:
Using the TI-84 Plus calculator:
z-score is z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
mean is 1535 grams and standard deviation is 169 grams.
(a) What proportion of broilers weigh between 1136 and 1243 grams?
For x = 1136 grams
z = (x-μ)/σ
= 1136 - 1535/169
= -2.36095
Determining the probability value from Z-Table:
= P(x = 1136)
= P(z =-2.36095)
= 0.0091142
For x = 1243 grams
z = (x-μ)/σ
= 1243 - 1535/169
= -1.72781
Determining the probability value from Z-Table:
P(x = 1243) = 0.042011
The proportion of broilers weigh between 1136 and 1243 grams is calculated as:
P(x = 1243) - P(x = 1136)
= 0.042011 - 0.0091142
= 0.0328968
≈ 0.0329
(b) What is the probability that a randomly selected broiler weighs more than 1600 grams?
For x = 1600 grams
z = (x-μ)/σ
= 1600 - 1535/169
= 0.38462
Determining the Probability value from Z-Table:
P(x<1600) = 0.64974
P(x>1600) = 1 - P(x<1600) = 0.35026
The probability that a randomly selected broiler weighs more than 1600 grams is 0.3502
(c) Is it unusual for a broiler to weigh more than 1710 grams?
For x = 1600 grams
z = (x - μ)/σ
= 1710 - 1535/169
= 1.0355
P-value from Z-Table:
P(x < 1710) = 0.84978
P(x > 1710) = 1 - P(x < 1710) = 0.15022
From the above calculation, it is not unusual for a broiler to weigh more than 1710 grams because 15.022% of the broilers weigh 1710 grams.
