7. Use R to answer the following question. Copy and paste the code and answer fr

Question

7. Use R to answer the following question. Copy and paste the code and answer from R into your paper. In a class of 100 students, 25 have hardcover and 75 students have paperback textbooks. If you randomly choose 10 students in this class, find the probability that 2 of them have hardcover texts. 8. A recent national study showed that approximately 44.7% of college students have used Wikipedia as a source in at least one of their term papers. Let X equal the number of students in a random sample of size n = 31 who have used Wikipedia as a source. Use R to answer parts b, c, d and e. a). What is the distribution for X. Give the distribution name and values for the parameters. b) Find the probability that X is equal to 17. c) Find the probability that X is at most 13. d) Find the probability that X is bigger than 11. e) Find the probability that X is between 16 and 19, inclusive. f) Give the mean of X, and standard deviation for X.

Explanation / Answer

Result:

7. Use R to answer the following question. Copy and paste the code and answer from R into your paper. In a class of 100 students, 25 have hardcover and 75 students have paperback textbooks. If you randomly choose 10 students in this class, find the probability that 2 of them have hardcover texts.

P=25/100=0.25

> dbinom(2, size=10, prob=0.25)

[1] 0.2815676

8. A recent national study showed that approximately 44.7% of college students have used Wikipedia as a source in at least one of their term papers. Let X equal the number of students in a random sample of size n = 31 who have used Wikipedia as a source. Use R to answer parts b, c, d and e.

a). What is the distribution for X. Give the distribution name and values for the parameters.

Binomial distribution.

n=31, p=0.447

b) Find the probability that X is equal to 17.

dbinom(17, size=31, prob=0.447)

[1] 0.07532248

c) Find the probability that X is at most 13.

P( x 13)

pbinom(13, size=31, prob=0.447)

[1] 0.451357

d) Find the probability that X is bigger than 11.

P( x >11) = 1- P( x 10)

1-pbinom(10, size=31, prob=0.447)

[1] 0.8882576

e) Find the probability that X is between 16 and 19, inclusive.

pbinom(19, size=31, prob=0.447)-pbinom(16, size=31, prob=0.447)

[1] 0.1488671

f) Give the mean of X, and standard deviation for X.

> n=31

> p=0.447

> #mean:

> n*p

[1] 13.857

> # standard deviation

> sqrt(n*p*(1-p))

[1] 2.768198

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