Question

6. Agriculture: Organic Tomatoes weighs 75 grams but 10 % of the tomatoes are too small! of 5 grams. It is reasonable to say the mean weight is 75 grams with a standard deviation of 5 grams. random sampling of nine organic farming community, found to have a sample mean weight of 85 grams.

a. Sample error for the Tomato organic farm yield: _____________________

b. Standard deviation of the sample mean: ____________

c. What is the probability of Tomato yield exceeding 80 grams for all Organic farms? d. Estimate the weight of all Tomatoes at the Organic farming Community.

Answer 1

a) sample error = Xbar - µ = 85-75 = 10

b) std error = σ/√n = 5/√9 = 1.67

c)

X =   80                                      
                                          
Z =   (X - µ )/(σ/√n) = (   80   -   75   ) / (    5   / √   9   ) = 3
                                          
P(X ≥   80   ) = P(Z ≥   3.00   ) =   P ( Z <   -3.000   ) =    0.0013           (answer)

excel formula for probability from z score is =NORMSDIST(Z)