mean 2600 and standard deviation 50. (a) Is total energy needed during pregnancy a qualitative variable or a quantitative variable? (b) What is the probability that a randomly selected pregnant woman has an energy need of more than 2625? (c) Describe the sampling distribution of X, the sample mean daily energy requirement for a random sample of 20 pregnant women.

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### Energy Needs During Pregnancy: Statistical Analysis

According to one association, the total energy needed during pregnancy is normally distributed, with a mean of 2600 and a standard deviation of 50.

**(a) Is total energy needed during pregnancy a qualitative variable or a quantitative variable?**

The total energy needed during pregnancy is a **quantitative variable** because it is measured numerically and can be subject to mathematical operations.

**(b) What is the probability that a randomly selected pregnant woman has an energy need of more than 2625?**

This requires calculating the probability that a normally distributed variable with a mean of 2600 and a standard deviation of 50 exceeds 2625.

**(c) Describe the sampling distribution of \(\bar{X}\), the sample mean daily energy requirement for a random sample of 20 pregnant women.**

The sampling distribution of the sample mean \(\bar{X}\) will also be normally distributed due to the Central Limit Theorem. The mean of the sampling distribution will be the same as the population mean (2600), and the standard deviation, known as the standard error, will be \(\frac{50}{\sqrt{20}}\).

**(d) What is the probability that a random sample of 20 pregnant women has a mean energy need of more than 2625?**

This requires calculating the probability that the sample mean \(\bar{X}\) exceeds 2625, given the aforementioned mean and standard error.

*Note: For (b) and (d), specific probability values would be calculated using statistical software or Z-tables.*
Transcribed Image Text:### Energy Needs During Pregnancy: Statistical Analysis According to one association, the total energy needed during pregnancy is normally distributed, with a mean of 2600 and a standard deviation of 50. **(a) Is total energy needed during pregnancy a qualitative variable or a quantitative variable?** The total energy needed during pregnancy is a **quantitative variable** because it is measured numerically and can be subject to mathematical operations. **(b) What is the probability that a randomly selected pregnant woman has an energy need of more than 2625?** This requires calculating the probability that a normally distributed variable with a mean of 2600 and a standard deviation of 50 exceeds 2625. **(c) Describe the sampling distribution of \(\bar{X}\), the sample mean daily energy requirement for a random sample of 20 pregnant women.** The sampling distribution of the sample mean \(\bar{X}\) will also be normally distributed due to the Central Limit Theorem. The mean of the sampling distribution will be the same as the population mean (2600), and the standard deviation, known as the standard error, will be \(\frac{50}{\sqrt{20}}\). **(d) What is the probability that a random sample of 20 pregnant women has a mean energy need of more than 2625?** This requires calculating the probability that the sample mean \(\bar{X}\) exceeds 2625, given the aforementioned mean and standard error. *Note: For (b) and (d), specific probability values would be calculated using statistical software or Z-tables.*
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