Question

6. A survey of U.S. adults found that 86% of those who use the Internet keep track of their online passwords in their heads. You randomly select 30 U.S. adults who use the Internet. Find the probability that the number who keep track of their online passwords in their heads is

(a) exactly 25

(b) more than 25

(c) less than 25

(d) identify any usual events, explain.

Answer 1

here this is binomial with parameter n=30 and p=0.86

a_)

P(X=25)=

(nCx)px(1−p)(n-x)    =

0.1766

if using ti-84 use command :binompdf(30,0.86,25)

if using excel use command :binomdist(25,30,0.86,false)

b)

P(X>25)=1-P(X<=25)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.5871

if using ti-84 use command :1-binomcdf(30,0.86,25)

if using excel use command :1-binomdist(25,30,0.86,true)

c)

P(X<25)=

∑x=024 (nCx)px(1−p)(n-x)    =

0.2363

if using ti-84 use command :binomcdf(30,0.86,24)

if using excel use command :binomdist(24,30,0.86,true)

d)

since each event has probability greater than 0.05, none of the above event is unusual