Question

The Spaaaarkling Toothpaste Company sells its product in 250 milliliter (ml) tubes. Due to a problem at the manufacturing plant, the individual tubes in a particular shipment have a mean amount of only 195 ml, a standard deviation of 38 ml, but still follow a Normal distribution. A store receives the defective shipment and offers to sell at a discount: 3 of the defective tubes for the price of 2.

1. In the defective shipment, what is the standard deviation of the average amount of toothpaste for all possible samples of 3 tubes?

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   Equation Editor (round this answer to exactly four decimal places, and use the rounded result for the rest of the problem).
2. If you take advantage of the sale and purchase 3 tubes (assumimg this to be a Simple Random Sample from the defective shipment), what is the probability that the average amount of toothpaste in your 3 tubes is less than 250 ml?

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   Equation Editor (round this answer to exactly four decimal places; do not convert to percent).
3. If you take advantage of the sale and purchase 3 tubes (assuming this to be a Simple Random Sample from the defective shipment), what is the probability that the average amount of toothpaste in your 3 tubes is more than 167 ml (in other words, you get a better price per ml by taking advantage of the sale)?

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   Equation Editor (round this answer to exactly four decimal places; do not convert to percent).

Answer 1