Final answer:
The student's question seeks to calculate the sample size needed for estimating the average number of books read, with 90% confidence, but lacks necessary data like standard deviation to complete the calculation.
Step-by-step explanation:
The student is asking how to determine the sample size needed to estimate the mean number of books read the previous year within one book, given a 90% confidence level. Unfortunately, the information provided does not include the standard deviation of the sample or the population which is required for calculating the sample size using the formula for the confidence interval of the mean. Typically, the formula for determining sample size (n) when the standard deviation (σ) is known and the margin of error (E) is specified is:
n = (Z*σ/E)²
Where:
- Z is the Z-score corresponding to the desired confidence level
- σ is the population standard deviation
- E is the desired margin of error
In this case, since the standard deviation is not given, we cannot complete the calculation. Typically, we would locate the Z-score for a 90% confidence level from the Z-table, square that value, multiply by the square of the population standard deviation, and divide by the square of the margin of error to compute the sample size.