I'm attempting to work out when to use the different formulas and how everything fits together, can you confirm if the following is correct?(adsbygoogle = window.adsbygoogle || []).push({});

1) If we had the problem: There are 250 dogs at a dog show who weigh an average of 12 pounds, with a standard deviation of 8 pounds. If 1 dog is chosen at random, what is the probability they will have a weight of greater than 8 pounds and less than 25 pounds?

Then we would use the formula: Z = (x-μ)/σ and use the z tables to work out our answer.

2) If we had the problem: There are 250 dogs at a dog show who weigh an average of 12 pounds, with a standard deviation of 8 pounds. If 4 dogs are chosen at random, what is the probability they will have an average weight of greater than 8 pounds and less than 25 pounds?

Then we would use the formula: Z = (x-μ)/(σ/√4) and use the z tables to work out our answer.

This is the same formula as the previous formula in 1), it's just that the squareroot of 1 is 1, so Z = (x-μ)/(σ/√1) became Z = (x-μ)/σ

3) If we had the problem: There are 29 dogs at a dog show who weigh an average of 12 pounds, with a standard deviation of 8 pounds. If 1 dog was chosen at random, what is the probability they will have an average weight of greater than 8 pounds and less than 25 pounds?

Then we would use the formula: tn-1 = (x-μ)/(σn-1/√1) = (x-μ)/(σn-1) and use the t tables to work out our answer.

4) If we had the problem: There are 29 dogs at a dog show who weigh an average of 12 pounds, with a standard deviation of 8 pounds. If 4 dogs are chosen at random, what is the probability they will have an average weight of greater than 8 pounds and less than 25 pounds?

Then we would use the formula: tn-1 = (x-μ)/(σn-1/√4) and use the t tables to work out our answer.

Is all of this correct?

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# Am I using these formulas properly? normal distribution+CLT

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