A Survey of an Introductory Statistics Class in Autumn 2003 $\quad\quad\quad\quad\quad\quad\quad\quad\text { Breakfast }$

question 12

Essay

A survey of an introductory statistics class in Autumn 2003 asked students whether or not they ate breakfast the morning of the survey. Results are as follows: $\quad\quad\quad\quad\quad\quad\quad\quad\text { Breakfast }$
$\text { Sex }\begin{array}{|c|c|c|c|}\hline & \text { Yes } & \text { No } & \text { Total } \\\hline \text { Male } & 66 & 66 & 132 \\\hline \text { Female } & 125 & 74 & 199 \\\hline \text { Total } & 191 & 140 & 331 \\\hline\end{array}$
a. What is the probability that a randomly selected student is female?
b. What is the probability that a randomly selected student ate breakfast?
c. What is the probability that a randomly selected student is a female who ate breakfast
d. What is the probability that a randomly selected student is female, given that the student
ate breakfast?
e. What is the probability that a randomly selected student ate breakfast, given that the student is female?
f. Does it appear that whether or not a student ate breakfast is independent of the student's sex? Explain.

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Definitions:

Neurodevelopmental Hypothesis

A theory suggesting that disorders like schizophrenia may originate from disruptions in the normal development of the nervous system during the prenatal period or early childhood.

Early Childhood

A crucial developmental phase typically referring to the period from birth up to the age of 8 years, focusing on physical, cognitive, and emotional growth.

Antipsychotic Drugs

Medications used to treat symptoms of severe psychological disorders, such as schizophrenia and bipolar disorder, by influencing neurotransmitter levels in the brain.

Schizophrenia

A psychiatric disorder that involves changes in how one thinks, perceives reality, feels emotions, and connects socially.