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Big chickens: The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1535 grams and standard deviation 169 grams. Use the TI-84 Plus calculator to answer the following. (a) What proportion of broilers weigh between 1136 and 1243 grams? (b) What is the probability that a randomly selected broiler weighs more than 1600 grams? (c) Is it unusual for a broiler to weigh more than 1710 grams? Round the answers to at least four decimal places. Part 1 of 3 The proportion of broilers that weigh between 1136 and 1243 grams is .

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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.