You flip an unbalanced coin 100 times. The probability that the coin lands on he

Question

You flip an unbalanced coin 100 times. The probability that the coin lands on heads is 0.3. Using the dbinom() function in R, calculate the probability that the coin lands on the heads side exactly 30 times out of the possible 100. You are teaching a class of eighty students. From experience, you know the probability that any one student passes the course is 0.95. Further, you assume that one student passing is independent from any other student passing. Using the pbinom() function in R, calculate the probability that the number of students (out of eighty that fail the course is greater than or equal to five students. Use the rbinom() function to create a vector of 10 random observations from the binomial distribution with n = 100 and probability of success is equal to 0.4. Calculate the summary statistics for this vector of random draws How do these numbers compare the expectation and variance of the binomial distribution when n = 100 and pi = 0.4? Make a histogram of this vector using the hist() command. Repeat question 3 but with 1,000 random draws. Comment on how the new sample mean compares to the population mean and the old sample mean. How does the histogram. differ?

Explanation / Answer

As multiple questions are posted, only the first one will be answered.

1. Using the following code:

dbinom(30, size=100, prob=0.3)

We get the following output:

0.0868

This is the probability coin lands on heads side exactly 30 out of 100 times.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.