---
title: "CSUEB Women's heights"
author: "Prof. Eric A. Suess"
date: "4/8/2024"
format: 
  html:
    self-contained: true
---

## CSUEB Women's heights

### Probability

Calculate the probability that a randomly CSUEB woman has height between 63 and 67 inches 

$$
P(63 \leq X \leq 67) = ?
$$

```{r}
pnorm(67, mean = 65, sd = 3) - pnorm(63, mean = 65, sd = 3)
```

```{r}
pnorm(0.67) - pnorm(-.67)
```

### Quantile

To find the minimum height to contact the top 5% of the population of CSUEB woman.

```{r}
qnorm(0.95)

qnorm(0.05, lower.tail = FALSE)
```

```{r}
qnorm(.95, mean = 65, sd = 3)

qnorm(.05, mean = 65, sd = 3, lower.tail = FALSE)
```