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 DeepSea Hydrothermal Vents After an Eruption" (Marine Biology, 2011: 181-192) proposed the following mixture of normal distributions as a model for the distribution of X 5 oocyte diameter (mm):
![](https://test.transtutors.com/qimg/91960522-3d96-47df-9f8f-1c087d3eb36d.png)
here f1 and f2 are normal pdfs. Suggested parameter![](https://test.transtutors.com/qimg/19c29c3a-694e-48f7-a37d-f8e7bf0edc74.png)
a. What is the expected (i.e. mean) value of oocyte diameter?
b. What is the probability that oocyte diameter is between 4.4 mm and 5.0 mm? [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
c. What is the probability that oocyte diameter is smaller than its mean value? What does this imply about the shape of the density curve?