Question

Is it plausible that the population distribution from which this sample was selected is normal? it plausible that the population distribution is normal. (x,x) (c) Predict the adjusted distribution volume of a single healthy individual by calculating a 95% prediction interval. (Round your answers to three decimal places.) How does this interval's width compare to the width of the interval calculated in part (b)? This interval's width is le! than the width of the interval calculated in part (b). You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

The population distribution is plausible to be normal based on the Central Limit Theorem. The 95% prediction interval can be calculated using the formula provided. The width of the interval can be compared to the width calculated in part (b).

Step-by-step explanation:

In order to determine whether the population distribution from which the sample was selected is normal, we can use the Central Limit Theorem. According to the Central Limit Theorem, when the sample size is large enough (usually greater than 30), the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. Since the sample size in this case is 48, which is larger than 30, it is plausible that the population distribution is normal.

To calculate a 95% prediction interval for the adjusted distribution volume of a single healthy individual, we can use the formula:

Prediction interval = sample mean ± (t-value) * (sample standard deviation / √n)

Where the t-value corresponds to the desired level of confidence (in this case, 95%) and n is the sample size. Using the given values, we can substitute them into the formula to calculate the prediction interval.

The width of the interval calculated in part (b) can be compared to the width of the interval calculated in this part (c) to determine if there is a difference in precision or uncertainty.