Freshman-sophomore retention rate (FSRR) for a college is the proportion of first-year students who return to the college for their sophomore year. Nationwide, the mean FSRR for colleges in the U.S. is 75%. Use the 68-95-99.7 rule to describe graphically the sampling distribution for the FSRR at college with entering classes of 400.
SD(p-hat)= sq. root of [(0.75*0.25)/400]= 0.022
So z= p-hat - p /SD(p-hat)
= ? - 0.75/0.022
I'm not sure what the first # should be where the ? mark is. In the book it gives it as like the proportion of say 15 out of 90 people are lefties. But I don't know about this problem. Please help ASAP!
To describe the sampling distribution for the FSRR at a college with entering classes of 400, you would need to calculate the standard deviation of the proportion and use the 68-95-99.7 rule.
The standard deviation of the proportion, denoted as SD(p-hat), can be calculated using the formula:
SD(p-hat) = sqrt[(p * (1-p)) / n]
For this problem, p represents the mean FSRR for colleges in the U.S., which is given as 0.75, and n represents the size of the sample, which is 400.
Calculating SD(p-hat):
SD(p-hat) = sqrt[(0.75 * (1-0.75)) / 400]
= sqrt[0.000703125]
≈ 0.0265
So the standard deviation of the proportion is approximately 0.0265.
To use the 68-95-99.7 rule, you can calculate the z-score using the formula:
z = (p-hat - p) / SD(p-hat)
In this case, you want to find the z-score for a specific proportion, denoted as p-hat. However, the specific proportion is not provided in the question. If you have information about the FSRR at the college, you can substitute that value for p-hat. Otherwise, you cannot calculate a specific z-score.
Once a specific z-score is determined, you can use the 68-95-99.7 rule to describe the graph of the sampling distribution. The rule states that approximately:
- 68% of the sample means will fall within 1 standard deviation (σ) of the population mean (p).
- 95% of the sample means will fall within 2 standard deviations (2σ) of the population mean.
- 99.7% of the sample means will fall within 3 standard deviations (3σ) of the population mean.
But without a specific p-hat value, we cannot provide a detailed graphical description.
To calculate the z-score for the sampling distribution of the freshman-sophomore retention rate (FSRR), we need to first have a specific proportion value to substitute into the formula.
In this case, the proportion value is the FSRR for a college with entering classes of 400. However, you mentioned that you are unsure about the first # in the formula. It seems like you don't have the proportion value needed to calculate the z-score.
To better understand the problem, let's clarify what information you have. Do you have any data about the retention rate for a specific college with entering classes of 400? If you do, please provide the data, and we can calculate the z-score based on that.