Statistics 1

In-Class Exercise 8

Yu-You Liou

Shih Chien University

2026-09-16

Question 1

Binomial Probabilities

A quiz has 12 multiple-choice questions, each with 4 options. A student guesses on every question, so p=0.25.

Compute in R with dbinom():

1. P(X=3)
2. P(X\le 3), using sum(dbinom(0:3, 12, 0.25))
3. P(X\ge 6)

Question 2

Mean and Standard Deviation of a Binomial Variable

For the same quiz:

1. Compute \mu=np and \sigma=\sqrt{npq} in R.
2. Would scoring 7 or more correct answers by guessing be unusual? Use the \mu\pm 2\sigma rule to justify your answer.

Question 3

Poisson Distribution

A help desk receives an average of 4 calls per hour.

Compute in R:

1. P(X=6) in a given hour with dpois()
2. P(X\le 2) with ppois()
3. P(X\ge 5)

State in one sentence which assumption of the Poisson distribution may be violated at lunchtime.