Using Excel to calculate binomial probabilities: (5 points) Suppose (as is rough

Question

Using Excel to calculate binomial probabilities:

(5 points) Suppose (as is roughly true) about 30% of all adult Internet users have posted videos online. A sample survey interviews an SRS of 1555 Internet users.

What is the actual distribution of the number of people in the sample who have posted videos online?

Use the excel function “BINOMDIST” to find the exact probability that 450 or fewer of the people in the sample have posted videos online.

Use the excel function “BINOMDIST” to find the exact probability that more than 470 (about 30.5%) of the people in the sample have posted videos online.

Use the excel function “BINOMDIST” to find the exact probability that between 440 and 460 of the people in the sample have posted videos online.

Explanation / Answer

p= propertion of adult internet users posted videos online. =0.30

n = number of adult internet users selected by simple random sampling = 1155

Let X denotes the number of people in the sample who have posted videos online

Hence X follows binomial distribution with parameters n =1155 and p =0.30

i) X ~ Bin(n=1155p=0.30)

ii) P( 450 or fewer of the peoplein the sample have posted videos online) = P( X<=450)

which cumulative probability at X =450

P(X<=450) = F(450)

Using Excel Function BINOMDIST

P(X<=450) =F(450) =BINOMDIST(450,1155,0.30,true) =1

iii) p=0.305

P(more than 470 people of the people in the sample have posted videos online) = P( X>470)

=1- P(X<=470)

= 1- F(470)

by using excel

F(470) = BINOMDIST(470,1155,0.305,true) = 1

P(X>470) = 1- P(X<=470) = 1-1 =0

iv) P(Between 440 and 460 of the people in the sample have posted videos online) = P(440 < X < 460)

=P(x<460) - P(x<440) = F(460) - F(440)

F(460) = BINOMDIST(460, 1155, 0.30, true) =1

F(440) = BINOMDIST(440, 1155, 0.30, true) =1

P(440 < X < 460) = 1-1 =0

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