Checking smartphone. A 2014 Bank of America survey of U.S. adults who own smartp

Question

Checking smartphone. A 2014 Bank of America survey of U.S. adults who own smartphones found that 35% of the respondents check their phones at least once an hour for each hour during the waking hours.^6 Such smartphone owners are classified as "constant checkers." Suppose you were to draw a random sample of 10 smartphone owners. The number in your sample who are constant checkers has a binomial distribution. What are n and p? Use the binomial formula to find the probability that exactly two of the 10 are constant checkers in your sampl Use the binomial formula to find the probability that two or fewer are constant checkers in your sample. What is the mean number of owners in such samples who are constant checkers? What is the standard deviation?

Explanation / Answer

Solution:

(a)

Let X be random variable representing constant checkers

n and p are parameters of binomial distribution

n=sample size=10

p=probability of success=35%=35/100=0.35

(b)need to find the probability

P(X=2)

P(X=2)=10 C2 (0.35)2 (1-0.35)10-2

   =10.9/2.1(0.35)2 (0.65)8

  P(X=2) = 0.1757

(c)P(two or fewer)= P(X <= 2)

=P(X=0)+P(X=1)+P(X=2)

=10c0(0.35)0 (1-0.35)10-0 +10C1(0.35)1(1-0.35)10-1  +10C2(0.35)2(1-0.35)10-2

  = 0.6510  +10*0.35*(0.65)9 +0.1757   

P(two or fewer) =0.2617

(d)mean =n.p

   =10(0.35)

mean =3.5

standard deviation=sqrt(np(1-p))

   =sqrt(10*0.35*(1-0.35))

   =sqrt(10*0.35*0.65)

     standard deviation =1.5083

  

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