Question

DISCRETE RANDOM VARIABLES Most smokers make multiple quit attempts before they stop smoking for good. The American Heart Association conducted a random experiment with 4,000 adult smokers. The number of attempts to stop smoking was recorded. The data are displayed in the table below. Number of Attempts to Stop Smoking PX=x) 05 .28 .3319 15 19 .15

Answer 1

Solution:

From the given table of probability distribution,

Probability of success of event "at least twice" is 0.33+0.19+0.15

i.e. 0.67

Consider this as the success probability for next calculation of binomial.

p = 0.67

10 adults are randomly selected.

So , n = 10

Let , X = No. of adults in sample that smoke at least twice.

X follows binomial(10 , 0.67)

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 4) = (₁₀ C ₄) * 0.67⁴ * (1 - 0.67)^10-4  

= 0.054

Answer is 0.054