Assume that a sample is used to estimate a population mean mu. use the given confidence level and sample data to find the margin of error. assume that the sample is a simple random sample and the population has a nominal distribution. round your answer to one more decimal place than the sample standard deviation. 99% confidence: n = 201: _x = 276, s = 75 16.0 13.8 12.4 10.5

i) 60 trees

ii) 3600 apples

Step-by-step explanation:

50 trees per acre

Total pounds produced per acre ( ideally ) = 70 * 50 = 3500 pounds

Assumption :

lets assume the additional tree = X

Therefore the number of trees planted per acre = ( 50 + x )  where x ≤ 30

calculate average yield per tree =   ( 70 - x )

Total yield per acre = number of trees * average yield per tree

                                 = ( 50 + x ) * ( 70 - x )

                           Y(x)   =  3500 + 20x - x^2

i) Number of trees that should be planted per acre to obtain maximum yield per acre

y'(x) = 20 - 2x = 0   hence X ( number of additional trees ) = 20 / 2 = 10

Number of trees that should be planted per acre = 50 + 10 = 60 trees

ii) Calculate maximum yield

where ; X = 10

number of trees planted per acre = ( 50 + x ) = 50 + 10 = 60

hence maximum yield  = ( 50 + x ) * ( 70 - x ) = ( 60 ) * ( 60 ) = 3600 apples