Question

(1 point) A scientist needs 20 specimens of Drosophila grimshawi (a type of fruitfly) for a study on its wing structure. Many different types of fruitfly inhabit an open area, and the process of capturing the number of specimens needed is to set several traps and then identify those that are D. grimshawi. The trapping procedure yields, on average 7 D. grimshawi for every 100 fruitflies captured. Let X be the random variable counting the number of fruitflies that must be captured to get the number needed for the study, and assume X has a negative binomial distribution. The process takes time, and the scientist can only afford to pay an assistant to capture up to 2 standard deviations more than the average number of trials needed to get the sample. Can the scientist get the necessary number of specimens if the assistant needs to capture 630 fruitflies? Answer the following the questions to answer this questions: px = Mx + 20x = Will scientist be able to get the sample necessary? (Enter yes or no)

Answer 1

px =7/100 =0.07

here mean of distribution=μ=r/p=

285.7143

standard deviation σ=√(r(1-p))/p=

61.6110

μ+2σx =408.9363

YEs