Question

Use a normal approximatoon to find the probability of a binomial random variable. Based on hestorical data, 11.6% of US adults curently smoked cinarettes In a separate survey of 250 adults, it is found that 19 curently smoked cigarettes Assuming that the 11.6% rate is correct for the US population, find the probability of geting 19 or fewner adults who currently smaked cigareties in the survey.

Answer 1

To find the probability of getting 19 or fewer adults who currently smoke cigarettes in the survey, we can use a normal approximation to the binomial distribution. By calculating the mean and standard deviation and using the z-score, we can find the probability. The probability is approximately 0.015 or 1.5%.

Step-by-step explanation:

To find the probability of getting 19 or fewer adults who currently smoke cigarettes in the survey, we can use a normal approximation to the binomial distribution. First, we need to calculate the mean and standard deviation of the binomial distribution.

Mean (μ) = n * p = 250 * 0.116 = 29

Standard Deviation (σ) = sqrt(n * p * (1 - p)) = sqrt(250 * 0.116 * (1 - 0.116)) = 4.5655 (rounded to four decimal places)

Next, we can use the normal distribution with mean 29 and standard deviation 4.5655 to find the probability of getting 19 or fewer adults who currently smoke cigarettes. We need to find the z-score of 19, which is calculated as (19 - μ) / σ = (19 - 29) / 4.5655 = -2.1856 (rounded to four decimal places).

Using a standard normal distribution table or a calculator, we can find that the probability of getting a z-score of -2.1856 or less is approximately 0.015 (or 1.5%). Therefore, the probability of getting 19 or fewer adults who currently smoke cigarettes in the survey is 0.015 or 1.5%.