The number of beetles in a lawn varies with an average of 1.3 per square yard. W

Question

The number of beetles in a lawn varies with an average of 1.3 per square yard. What is the approximate probability of obtaining a sample of 10 yd.² of one with more than 10 Beatles? The number of beetles in a lawn varies with an average of 1.3 per square yard. What is the approximate probability of obtaining a sample of 10 yd.² of one with more than 10 Beatles? The number of beetles in a lawn varies with an average of 1.3 per square yard. What is the approximate probability of obtaining a sample of 10 yd.² of one with more than 10 Beatles?

Explanation / Answer

As in 1 yd^2 there are 1.3 beetles, then, at 10 yd^2, there are 1.3*10 = 13 beetles on the average.

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    13      
          
x = our critical value of successes =    10      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   10   ) =    0.251682027
          
Thus, the probability of at least   11   successes is  
          
P(more than   10   ) =    0.748317973 [answer]

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.