Question

How will marketers change their social media use in the near future? A survey by Social Media Examiner reported that 76% of B2B marketers (marketers that focus primarily on attracting businesses) plan to increase their use of LinkedIn, as compared to 52% of B2C marketers (marketers that primarily target consumers). The survey was based on 1,780 B2B marketers and 3,306 B2C marketers (let’s assume the survey data are the population). The following table summarizes the results:

Business focus

Increase use of LinkedIn? B2B B2C Total

Yes 1,353 1,719 3,072

No 427 1,587 2,014

Total 1,780 3,306 5,086

(e) If 10 marketers out of 5,086 survey respondents were selected at random as a sample, what

is the probability that 7 B2B marketers are included in the same? (use the binomial

distribution with the parameter ? from the survey data)
(f) If 200 marketers out of 5,086 survey respondents were selected at random as a sample, what

is the probability that the proportion of B2B marketers in the sample is between 100 and 140 (i.e., 50 to 70%)? (use the normal distribution based on the central limit theorem)

Answer 1

e)

here probability of B2B marketers ?=1780/5086=0.34998~ 0.350

hence from binomial distribution:

probability that from 10 marketers 7 B2B marketers are included =P(X=7)

= =0.0212

f)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.350
sample size       =n=	200
std error of proportion=σp=√(p*(1-p)/n)=	0.0337

hence  based on the central limit theorem ;  probability that the proportion of B2B marketers  is between 50 to 70%:

probability =

P(0.5<X<0.7)

=

P(4.45<Z<10.38)~

1.0000-1.0000=

0.0000

( please revert for any clarification required)