Question

Suppose that 10% of the fields in a given agricultural area with about 2,500 fields are infested with the sweet potato white fly. One hundred fields in this area are randomly selected and checked for whitefly.

Required:
a. What is the average number of fields sampled that are infested with whitefly?
b. Within what limits would you expect to find the number of infested fields, with probability approximately 95%?
c. What might you conclude if you found that x=25 fields were infested? Is it possible that one of the characteristics of a binomial experiment is not satisfied in this experiment? Explain.

Answer 1

a. 250 fields

b. 220 to 280 fields

c. Fields are not independent

Explanation:

a. The average number of fields sampled that are infested with whitefly =

number of fields X Percentage sampled, 10%

= 2500 X 10% = 250 fields

b. Going by the binomial distribution is the square of the standard deviation, divided by (the product of the sample size n, and the probability a and b). While the standard deviation is the square root of the variance

σ = √nab

= √na(1-a) = √2500 X 10% X (1- 10%)

= √225 = 15

Now let's use the empirical rule that says about 95% of the observations are within two standard deviations from the mean since the number of trials is very large

μ - 2σ = 250 - 2(15) = 220

μ + 2σ = 250 + 2(15) = 280

Approximately 220 to 280 fields are expected to be infested going by 95% probability observation

c. Since x=25 is considered small and is not captured within 220 and 280 fields making one of the characteristics of binomial experiment not satisfied which expects each field to be independent. Making fields that are close together more likely to be infected.