Question

The distribution of weights of Idaho baking potatoes is Normal with mean 0.78 pounds and
standard deviation of 0.09 pounds.

A restaurant chain uses potatoes over 0.90 pounds in its Cheesy Potato appetizer special.

2. The chain needs 1000 potatoes per week for this special. To obtain this quantity, how many
potatoes (of all weights) should be ordered per week?

3. The chain also must discard potatoes that are too small. They’ve learned that 0.5% (1⁄2 of 1%)
of all potatoes are discarded. What are the weights of the discarded potatoes? Answer in a
complete sentence that describes the weight condition for discarding a potato. (Express any
weight to at least the nearest 0.001 pound.)

4. For the order size you obtained in 2: How many of the potatoes are discarded?

5. Potatoes not discarded, and not used for a Cheesy Potato, become french fries. How many
potatoes become french fries each week?

Answer 1

Answer:

Based on the given information, the distribution of weights of Idanho baking potatoes is Normal

• Mean = 0.78 pounds
• Standard deviation = 0.09 pounds

2) The chain needs 1000 potatoes per week for this special. To obtain this quantity, how many potatoes (of all weights) should be ordered per week?

• Weight of potato in Potato appetizer special = 0.9 pounds
• Number of potatos required per week for this special = 1000
• Total weight of potatos required per week for this special = 0.9*1000 = 900 pounds
• Mean weight of potatos = 0.78 pounds
• Since the distribution of weight of potato is Normal, therefore probability of finding potato that weigh more than 0.9 pounds can be determined by calculating the Z value.
• Z = (0.9 - 0.78) / (0.09) = 1.333
• Probability associated with P(x > 0.9) = P(Z > 0.9) = 0.0913
• This means, that 9.13% of the entire lot of potatos will have potato that each weigh more than 0.9 pounds
• Therefore Number of potatos (of all weight) that needs to be ordered per week so that they contain 1000 potatos weighing more than 0.9 pounds is = (1000/9.13%) = 10953
• Hence, 10953 potatoes needs to be ordered so that the lot would contain around 1000 potatoes that weigh more than 0.9 pounds and could be used for making Cheesy potato appetizer special.

3. The chain also must discard potatoes that are too small. They’ve learned that 0.5% (1⁄2 of 1%)
of all potatoes are discarded. What are the weights of the discarded potatoes? Answer in a
complete sentence that describes the weight condition for discarding a potato. (Express any
weight to at least the nearest 0.001 pound.)

• Total number of potatoes ordered =10953
• Mean weight of potatoes = 0.78 pounds
• Percentage of potatoes that are too small = 0.5%
• Number of potatoes that are discarded = 0.5%*10953 = 54.7 or ~55.
• Z-value corresponding to 0.005 is -2.576 (left tailed)
  X-value corresponding to Z value of -2.576 is = mean + sigma*Z = 0.78 + (-2.576*0.09) = 0.548 pounds
• Weight of potatoes discarded = 55 * 0.548 = < 30.148 or ~30 pounds
• So overall weight of potatoes that are discarded will weigh less than 30.148 pounds

4. For the order size you obtained in 2: How many of the potatoes are discarded?

• Total number of potatoes ordered =10953
• Percentage of potatoes that are too small = 0.5%
• Number of potatoes that are discarded = 0.5%*10953 = 54.7 or ~55.
• Therefore, ~55 potatoes are usually discarded being too small.

5. Potatoes not discarded, and not used for a Cheesy Potato, become french fries. How many
potatoes become french fries each week?

• The weight of pototoes that lie between 0.548 pounds and 0.9 pounds will not be used as chessy potato and will also not be discarded.
• Probability (0.548< x < 0.9) = 0.9038
• Number of potatos that can be used to make french fries = 0.9038*10953 = 9899.3 or ~9900 potatoes