Question

# A. What is the probability that 2 ​smartphone-dependent? B. What is the probability that at least...

A. What is the probability that 2 ​smartphone-dependent?

B. What is the probability that at least 4 are​smartphone-dependent?

C. What is the probability that at most 1 is​smartphone-dependent?

D. If you selected a sample in a particular geographic area and found that none of the 12 respondents are​ smartphone-dependent, what conclusions might you reach about whether the percentage of​smartphone-dependent young adults in this area was 13​%?

Given,

n = 12

p = 13% = 0.13

Let us utilize the binomial distribution

a)

To determine the probability that 2 smartphone dependent

P(X = 2) = 12C2 * 0.13^2* (1-0.13)^(12-2)

= 66*0.13^2*0.87^10

= 0.277

b)

To determine the probability that at least 4 are​smartphone-dependent

P(X >= 4) = 1 - P(X = 4)

= 1 - [12C0*0.13^0*0.87^13 + 12C1*0.13^1*0.87^11 + 12C2*0.13^2*0.87^10 + 12C3*0.13^3*0.87^9]

= 1 - [0.1636 + 0.3372 + 0.2771 + 0.1380]

= 1 - 0.9159

= 0.0841

c)

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

= 0.5252

d)

Here we may not reject the 0.13 which is due to that sample of 12 is not the overall population representative.

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