Question

A recent survey reported that 41​% of​ 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.

Answer 1

here this is binomial with parameter n=6 and p=0.41

a)

P(X=4)=

(nCx)px(1−p)(n-x)    =

0.1475

b)

P(X=6)=

(nCx)px(1−p)(n-x)    =

0.0048

c)

P(X>=4)=1-P(X<=3)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.1933

d)

mean E(x)=μ=np=2.46

standard deviation σ=√(np(1-p))=1.2047

e)

Correct options are:

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.

outcomes are mutually exclusive and completely exhaustive