A study of peach trees found that the average number of peaches per tree was 1025. The standard deviation of the population is 35 peaches per tree. A scientist wishes to find the 99% confidence interval for the mean number of peaches per tree. How many trees does she need to sample to obtain an average accurate to within 18 peaches per tree

Question

Mathematics

Preston Townsend

17 August, 15:32

A study of peach trees found that the average number of peaches per tree was 1025. The standard deviation of the population is 35 peaches per tree. A scientist wishes to find the 99% confidence interval for the mean number of peaches per tree. How many trees does she need to sample to obtain an average accurate to within 18 peaches per tree

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Jovany Medina · Answer 1

26 trees

Step-by-step explanation:

Mean = 1025

Standard deviation = 35

Confidence interval = 99%

Margin error = 18

From the table, 99% = 2.58

n = [Zcritical (Standard deviation / margin error) ]^2

n = [2.58 (35/18) ]^2

n = (5.0167) ^2

n = 26 (to the nearest highest integer)

n = 26 trees