In order to shorten the length of the confidence interval by half without changing the confidence level, the value of (σ / (number of samples^{0.5})) should be halved. Given that σ is the constant value, the number of samples needs to be increased, so that (new number of samples^{0.5}) / (number of samples^{0.5}) is equal to 2. Considering that the number of samples is 100, the new number of samples should be increased to 400 apples. In such a case, (400^{0.5}) / (100^{0.5}) is equal to 2.

# You sample 100 apples from your farm’s harvest of over 200,000 apples. The mean weight of the sample is 112 grams. Let’s assume that you know the weight of all apples produced by your farm is normally distributed and the standard deviation of the weight is 40 grams. What is the 99% confidence interval for the mean weight of apples of your farm? If we want to shorten the length of the confidence interval by half while keeping the same confidence level at 99%, how many apples should we sample to begin with?

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*Academic.Tips*. (2021) 'You sample 100 apples from your farm's harvest of over 200,000 apples. The mean weight of the sample is 112 grams. Let's assume that you know the weight of all apples produced by your farm is normally distributed and the standard deviation of the weight is 40 grams. What is the 99% confidence interval for the mean weight of apples of your farm? If we want to shorten the length of the confidence interval by half while keeping the same confidence level at 99%, how many apples should we sample to begin with'. 25 September.

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Academic.Tips. (2021, September 25). *You sample 100 apples from your farm's harvest of over 200,000 apples. The mean weight of the sample is 112 grams. Let's assume that you know the weight of all apples produced by your farm is normally distributed and the standard deviation of the weight is 40 grams. What is the 99% confidence interval for the mean weight of apples of your farm? If we want to shorten the length of the confidence interval by half while keeping the same confidence level at 99%, how many apples should we sample to begin with?* Retrieved from https://academic.tips/question/you-sample-100-apples-from-your-farms-harvest-of-over-200000-apples-the-mean-weight-of-the-sample-is-112-grams-lets-assume-that-you-know-the-weight-of-all-apples-produced-by-your-farm-is-normal/

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*Academic.Tips*. 2021. "You sample 100 apples from your farm's harvest of over 200,000 apples. The mean weight of the sample is 112 grams. Let's assume that you know the weight of all apples produced by your farm is normally distributed and the standard deviation of the weight is 40 grams. What is the 99% confidence interval for the mean weight of apples of your farm? If we want to shorten the length of the confidence interval by half while keeping the same confidence level at 99%, how many apples should we sample to begin with?" September 25, 2021. https://academic.tips/question/you-sample-100-apples-from-your-farms-harvest-of-over-200000-apples-the-mean-weight-of-the-sample-is-112-grams-lets-assume-that-you-know-the-weight-of-all-apples-produced-by-your-farm-is-normal/.

1. *Academic.Tips*. "You sample 100 apples from your farm's harvest of over 200,000 apples. The mean weight of the sample is 112 grams. Let's assume that you know the weight of all apples produced by your farm is normally distributed and the standard deviation of the weight is 40 grams. What is the 99% confidence interval for the mean weight of apples of your farm? If we want to shorten the length of the confidence interval by half while keeping the same confidence level at 99%, how many apples should we sample to begin with?" September 25, 2021. https://academic.tips/question/you-sample-100-apples-from-your-farms-harvest-of-over-200000-apples-the-mean-weight-of-the-sample-is-112-grams-lets-assume-that-you-know-the-weight-of-all-apples-produced-by-your-farm-is-normal/.

Bibliography

*Academic.Tips*. "You sample 100 apples from your farm's harvest of over 200,000 apples. The mean weight of the sample is 112 grams. Let's assume that you know the weight of all apples produced by your farm is normally distributed and the standard deviation of the weight is 40 grams. What is the 99% confidence interval for the mean weight of apples of your farm? If we want to shorten the length of the confidence interval by half while keeping the same confidence level at 99%, how many apples should we sample to begin with?" September 25, 2021. https://academic.tips/question/you-sample-100-apples-from-your-farms-harvest-of-over-200000-apples-the-mean-weight-of-the-sample-is-112-grams-lets-assume-that-you-know-the-weight-of-all-apples-produced-by-your-farm-is-normal/.

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"You sample 100 apples from your farm's harvest of over 200,000 apples. The mean weight of the sample is 112 grams. Let's assume that you know the weight of all apples produced by your farm is normally distributed and the standard deviation of the weight is 40 grams. What is the 99% confidence interval for the mean weight of apples of your farm? If we want to shorten the length of the confidence interval by half while keeping the same confidence level at 99%, how many apples should we sample to begin with?" *Academic.Tips*, 25 Sept. 2021, academic.tips/question/you-sample-100-apples-from-your-farms-harvest-of-over-200000-apples-the-mean-weight-of-the-sample-is-112-grams-lets-assume-that-you-know-the-weight-of-all-apples-produced-by-your-farm-is-normal/.