A researcher collects data on a population of red squirrels by placing overnight

Question

A researcher collects data on a population of red squirrels by placing overnight Sherman live traps every 10 m along transects in a forest. When she catches a squirrel, she makes some measurements, determines the sex of the rodent, places a uniquely numbered leg band on its left leg, and releases the animal. After the first night, she caught 30 squirrels. 15 of these 30 squirrels are males. Previous research indicated that the sex ratio of males to females in this population is approximately 40:60. If this is true, what is the probability of catching 15 male squirrels in a sample of 30 (assuming all squirrels have equal probability of capture)?

Explanation / Answer

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    30      
p = the probability of a success =    0.4      
x = the number of successes =    15      
          
Thus, the probability is          
          
P (    15   ) =    0.07831221 [ANSWER]

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