According to a 2013 study by the Pew Research Center, 15% of adults in the United States do not use the Internet (Pew Research Center website, December, 15, 2014). Suppose that 10 adults in the United States are selected randomly a. Is the selection of the 10 adults a binomial experiment? - Select your answer Explain The input in the box below will not be graded, but may be reviewed and considered by your instructor. b. What is the probability that none of the adults use the Internet (to 4 decimals)? c. What is the probability that 3 of the adults use the Internet (to 4 decimals)? If you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations d. What is the probability that at least 1 of the adults uses the Internet (to 4 decimals)?

Step-by-step explanation:

Hello!

The study states that 15% of adults in the U.S. do not use the internet.

A sample of 10 adults was taken.

The study variable is:

X: Number of adults of the U.S. that do not use the internet.

a.

To see if this is a binomial experiment, we have to check if it follows the binomial criteria.

This variable has two possible outcomes, that "the adult doesn't use the internet", this will be the success of the experiment, and that "the adult uses the internet", this will be the failure of the experiment.

The number of observations of the trial is fixed. n= 10 adults.

Each observation in the trial is independent, this means that none of the trials will affect the probability of the next trial. There is no information to suggest otherwise and adults were chosen randomly so we will consider them independent of each other.

The probability of success in the same from one trial to another. The proportion of adults that don't use the internet is p=0.15

All conditions are met, so we can say this is a binomial experiment and the variable has binomial distribution So X≈ Bi (n;ρ)

b. You need to calculate the probability that none of the adults uses the internet in a sample of 10 since our variable counts the adults that do not use the internet, we need to calculate the probability of X=10:

Note: you can calculate this manually or use tables of cumulative probabilities for the binomial distribution. If you have the tables on hand, it is easier and faster to calculate the asked probabilities with the tables:

P(X=10)= P(X≤10) - P(X≤9)

To calculate the probability of an observation of the variable, you have to look for the accumulated probability until that number and subtract what's accumulated until the previous integer.

P(X=10)= P(X≤10) - P(X≤9)= 1 - 0.9999= 0.0001

c.

You need to calculate the probability of 3 adults using the internet, this means that if 3 out of 10 use the internet, then 7 do not use the internet.

Let Y be the number of adults that uses the internet (This variable is the complement of X), then:

P(Y=3) = P(X=7)

P(X=7)= P(X≤7) - P(X≤6)= 0.9999 - 0.9998= 0.0001

d.

You need to calculate the probability of at least one adult using the internet, symbolically Y ≥ 1. Now if "at least 1 adult uses the internet" then we will expect that "at most 9 adults don't use the internet", symbolically X ≤ 9.

P(Y ≥ 1)= P(X ≤ 9)= 0.9999

I hope it helps!

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