Please answer a,b,c,d. Thanks! 5.37 Smartphone adoption among American teens has

Question

Please answer a,b,c,d. Thanks!

5.37 Smartphone adoption among American teens has increased substantially, and mobile access to the Internet is pervasive. One in four teenagers are "cell mostly" Internet users-that is, they mostly go online using their phone and not using some other de- vice such as a desktop or laptop computer. (Source: Teens and Technology 2013, Pew Research Center, bit.ly/101ciF1.) If a sample of 10 American teens is selected, what is the prob- ability that a. 4 are "cell mostly" Internet users? b. at least 4 are "cell mostly" Internet users? c. at most 8 are "cell mostly" Internet users? If you selected the sample in a particular geographical ar and found that none of the 10 respondents are "cell mostly Internet users, what conclusions might you reach about whether the percentage of "cell mostly" Internet users in this 23 area was 25%?

Explanation / Answer

a)

N=10

P=0.25

1-P=0.75

Probability that 4 are users "cell-mostly"

Required Prob = C(10,4)*(0.25)^4*(0.75)^6 = 0.145

b) At least 4

P(X=5)+P(X=6)+....P(X=10)

= 1- {P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)}

= 1-{0.056+0.187+0.281+0.250+0.145}

= 1-0.919

= 0.081

c)

At Most 8

1- {P(X=9)+P(X=10)}

= 1- {0.00002861+0.000000953}

= 0.99997

d)

P(X=0) = 0.75^10 = 0.0563

If it is 0.25

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