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For the leopard gecko (Eublepharis macularius), the gender of their offspring is determined by the temperature...

For the leopard gecko (Eublepharis macularius), the gender of their offspring is determined by the temperature during embryonic development. Researchers determined that at 31 degrees C, the proportion of males produced is 35%. They have 6 leopard gecko embryos that have been incubated at 31 degrees C and will soon hatch. Set up the formula to compute the probability of getting 2 or fewer males.

Expert Solution

Binomial Distribution is being used to compute the the probability of getting 2 or fewer males.

Binomial Distribution

If 'X' is the random variable representing the number of successes, the probability of getting ‘r’ successes and ‘n-r’ failures, in 'n' trails, ‘p’ probability of success ‘q’=(1-p) is given by the probability function

For the given problem

X : Number of males produced (Number of successes)

p : Probability of a male produced at 31 degrees C (Probability of success)

Researchers determined that at 31 degrees C, the proportion of males produced is 35% i.e p = 35/100 = 0.35

q = 1-p = 1-0.35 = 0.65

n : Number of trails ; leopard gecko embryos that have been incubated at 31 degrees C and will soon hatch = 6

By Binomial distribution,

Probability of getting 'r' males is given by the following probability function;

Probability of getting 2 or fewer males :

milcah answered 1 year ago

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