Question

In: Statistics and Probability

3. Workers at an orchard recorded the weights of 1000 avocados. The weights are approximately normally...

3. Workers at an orchard recorded the weights of 1000 avocados. The weights are approximately normally distributed, with a mean weight of 225 grams and a standard deviation of 25 grams. Which of the following statements are true? Select all that apply.

A. Approximately 34% of the avocados weight between 225 and 250 grams. B. Approximately 50% of the avocados weigh 225 grams.

C. Approximately 500 of the avocados weigh more than 200 grams.

D. Approximately 160 avocados weigh more than 250 grams.

E. Approximately 84% of the avocados weigh less than 250 grams.

Expert Solution

Let X denotes the weight of a randomly selected worker.

X ~ Normal(225, 25²)

A)

So, Approximately 34% of the avocados weight between 225 and 250 grams.

B)

So, Approximately 50% of the avocados weigh 225 grams.

C)

Number of avocados weigh more than 200 grams = 1000*0.8413 = 841.3

D)

Number of avocados weigh more than 250 grams = 100*0.1587 = 158.7 160

E)

Approximately 84% of the avocados weigh less than 250 grams.

Hence,

The TRUE statements are -

A. Approximately 34% of the avocados weight between 225 and 250 grams.

B. Approximately 50% of the avocados weigh 225 grams.

D. Approximately 160 avocados weigh more than 250 grams.

E. Approximately 84% of the avocados weigh less than 250 grams.

orchestra answered 2 years ago

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