the_problem = {
if (name == "") {
return md``;
} else {
return md`---
Suppose that ${tex`X`} is a normally distributed random variable with mean ${tex.block`\mu=${f(
p.m
)} \: \text{ and } \: \sigma = ${f(p.s)}.`}
1. Compute the ${tex`Z`}-score for ${tex`X=${f(
p.m + p.s
)}`}. Then, use the rules of thumb to tell us ${tex.block`P(X<${f(
p.m + p.s
)}).`}
2. Use a ${tex`Z`}-score and a normal table to compute each of the following:
* a: ${tex`P(X<${f(p.x1)})`}
* b: ${tex`P(X>${f(p.x1)})`}
* c: ${tex`P(${f(p.x2)}<X<${f(p.x1)})`}
3. Now, fire up [this Colab notebook](https://colab.research.google.com/drive/1s1OXSsXmtTGghfCi1uhqe2-_W1y5MyDr?usp=sharing) and use it to:
* a: Draw a picture of your normal distribution together with a verticaal line indicating the location of ${tex`X=${f(
p.x1
)}`}
* b: Use the \`norm.cdf\` command to compute ${tex`P(X<${f(
p.x1
)})`}. Note that this is the same computation you did in 2a. How do your answers compare?
`;
}
}