People were polled on how many books they read the previous year. How many subjects are needed to estimate the number of books read the previous year within one book with 90% confidence?

Initial survey results indicate that standard deviation= 15.5 books.

To estimate the required sample size, we can use the formula for the sample size in a confidence interval estimation:

n = (Z * σ / E)^2

where:
n = sample size
Z = Z-score (the value that corresponds to the desired confidence level, in this case, 90%)
σ = population standard deviation (15.5 books)
E = margin of error (1 book)

For a 90% confidence level, the Z-score is 1.645.

n = (1.645 * 15.5 / 1)^2
n ≈ (25.4975)^2
n ≈ 649.898

Since we cannot have a fraction of a subject, we round up to the nearest whole number.

n ≈ 650 subjects

Therefore, 650 subjects are needed to estimate the number of books read within one book with 90% confidence.

To estimate the number of books read the previous year within one book with 90% confidence, you need to determine the required sample size. The formula to calculate the sample size needed for estimating the mean with a specified level of confidence is:

n = (Z * σ / E)^2

Where:
n = Sample size needed
Z = Z-score corresponding to the desired level of confidence (in this case, for a 90% confidence level, Z ≈ 1.645)
σ = Standard deviation of the population
E = Maximum error or margin of error (in this case, within one book)

Plugging in the values given:
Z = 1.645
σ = 15.5
E = 1

n = (1.645 * 15.5 / 1)^2
n ≈ (25.5075)^2
n ≈ 650.802

Therefore, to estimate the number of books read the previous year within one book with 90% confidence, approximately 651 subjects are needed.