Question

A recent survey reported that 57% to 18 to 29 year olds in a certain country own tablets. Using the binomial distribution , complete parts a through e below.

a. What is the probability that in the next six​ 18- to​ 29-year-olds surveyed, four will own a​ tablet?

b. What is the probability that in the next six? 18- to? 29-year-olds surveyed, all six will own a? tablet?

c. What is the probability that in the next six? 18- to? 29-year-olds surveyed, at least four will own a? tablet?

d. What are the mean and standard deviation of the number of? 18- to? 29-year-olds who will own a tablet in a survey of? six?

e. What assumptions do you need to make in? (a) through? (c)? Select all that apply.

-The outcome of any observation is independent of the outcome of any other observation.

-The probability of an observation being classified as the event of? interest,

pi??, is constant from observation to observation.

-The outcome of any observation is dependent of the outcome of any other observation.

-Each observation is classified into one of two mutually exclusive and collectively exhaustive categories.

Answer 1

GIVEN THAT :-

According to the question we have that ,

A survey reported that 57% to 18 to 29 year olds in a certain country own tablets.

TO FIND :A)What is the probability that in the next six​ 18- to​29-year-olds surveyed, four will own a​ tablet?

now from the question we have that

n=6 ,x= 4, p= 0.57 and

q=1-p

=1-0.57

= 0.43

q=0.43

TO FIND :A)What is the probability that in the next six​ 18- to​29-year-olds surveyed, four will own a​ tablet?

for finding the P(X=4) we have a formula

P(X=4)= Ncx*p^x*q^n-x.

substituting the values and solving we get that

= 0.2928 =BINOMDIST (4,6,0.57,FALSE)

TO FIND :B) What is the probability that in the next six​ 18- to​29-year-olds surveyed, all six will own a​ tablet?

So from the above we use the same formula and the same values for finding the P(X=6)

P(X=6)= Ncx*p^x*q^n-x

= 0.0343

TO FIND :C)What is the probability that in the next six​ 18- to​29-year-olds surveyed, at least four will own a​ tablet?

So as from the above we use the formula and the same values

P(X>=4)

=1- BINOMDIST(3,6,0.57,TRUE)

= 0.48

TO FIND :D)What are the mean and standard deviation of the number of​18- to​ 29-year-olds who will own a tablet in a survey of​ six?

for finding the mean we have a formula mean =np

n=6 ;p=0.57

there fore n*p =6*0.57

mean = 3.42

now for finding the variance we have a formula variance =npq

n=6 ;p=0.57;q=0.43 from the above substituting we get that

=6*0.57*0.43

variance =1.4706

now for finding the standared deviation we have a formula = sqrt(variance)

=sqrt (1.4706) from the above

standared deviation =1.2127

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