A consumer advocate claims that 70 percent of cable television subscribers are n

Question

A consumer advocate claims that 70 percent of cable television subscribers are not satisfiedwith their cable service, and suppose that a random sample of 25 cable subscribers is selected.Let x be the number of cable television subscribers who are not satisfied with their cable service.

Find the probability (in DECIMAL format) that

a) More than 20 subscribers are not satisfied with their service, Note: round to the THIRD decimal place.

b) 14 to 18 subscribers (inclusive) are not satisfied with their service, Note: round to the THIRD decimal place.

c) Find the mean of x

d) Find the standard deviation of x, Note: round to the THIRD decimal place.

Explanation / Answer

a) 70% of cable subscribers are not satisfied with their cable service. So probability that a randomly chosen customer is not satisfied with their cable service is 0.7

So the number X of 25 randomly chosen customers who are notsatisfied with their cable service has a Binomial(25,0.7) distribution. So we want to calculate P(X>20) where X has Binomial(25,0.7) distribution.

P(X>20)=0.090

b) This is P(14<=X<=18) an is equal to 0.615.

c) Mean of X is 25 x 0.7 = 17.5

d) Variance of X is 25 x 0.7 x (1-0.7) = 5.25, So standard deviation is its square root, 2.291

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