Question

The weight of competition pumpkins at the Anamosa Pumpkinfest in Anamosa, Iowa can be represented by...

The weight of competition pumpkins at the Anamosa Pumpkinfest in Anamosa, Iowa can be represented by a normal distribution with a mean of 703 pounds and a standard deviation of 347 pounds.

A. Find the probability that a randomly selected pumpkin weighs at least 1000 pounds.

B. Find the probability that a randomly selected pumpkin weighs less than 750 pounds.

C. Find the probability that a randomly selected pumpkin weighs between 500 and 900 pounds.

D. Find the probability that the average weight of a randomly selected sample of 10pumpkins is less than 650 pounds

Math   Statistics-And-Probability   
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Answer #1

Z is the standard normal variable

The weight of competition pumpkins are normal distribution with a mean of 703 pounds and a standard deviation of 347 pounds

= 703 (mean)

= 347 (standard deviation)

A.

Z-score for 1000 pounds =

we get the value of from z table

Answer: The probability that a randomly selected pumpkin weighs at least 1000 pounds is 0.1949

B.

Z-score for 750 pounds =

we get the value of from z table

Answer: The probability that a randomly selected pumpkin weighs less than 750 pounds is 0.5557

C.

Z-score for 500 pounds =

Z-score for 900 pounds =

we get the value of and from z table

Answer: The probability that a randomly selected pumpkin weighs between 500 and 900 pounds is 0.4381

D.

n = 10 (sample size)

The average weight of competition pumpkins follows normal distribution with a mean of 703 pounds and a standard deviation of    pounds

= 703 (mean)

is the standard deviation of the sample

Z-score for 650 pounds =

we get the value of from z table

Answer: The probability that the average weight of a randomly selected sample of 10 pumpkins is less than 650 pounds is 0.3156

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