An oocyte is a female germ cell involved in reproduction. Based on analyses of a large sample, the article “Reproductive Traits of Pioneer Gastropod Species Colonizing Deep-Sea Hydrothermal Vents After an Eruption” (Marine Biology, 2011: 181–192) proposed the following mixture of
f(x) = pf1(x; µ1, σ) + (1 − p) f2(x; µ2, σ)
where f1 and f2 are normal pdfs. Suggested parameter values were p = .35, µ1 = 4.4, µ2 = 5.0, and σ = .27.
a. What is the expected (i.e. mean) value of oocyte diameter?
b. What is the probability that oocyte diameter is between 4.4 µm and 5.0 µm? [Hint: Write an expression for the corresponding integral, carry the integral operation through to the two components, and then use the fact that each component is a normal
c. What is the probability that oocyte diameter is smaller than its
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