Question

Use a normal approximation to find the probability of a binomial random variable. Based on historical data, 11.6% of US adults currently smoked cigarettes. In a separate survey of 250 adults, it is found that 19 currently smoked cigarettes. Assuming that the 11.6% rate is correct for the US population, find the probability of getting 19 or fewer adults who currently smoked cigarettes in the survey.

A. 0.905
B. 0.095
C. 0.977
D. 0.023

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.

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. First, we calculate the mean and standard deviation of the binomial distribution. The mean, or expected value, is given by np where n is the sample size (250) and p is the proportion of adults who smoke (0.116). The standard deviation is given by sqrt(np(1-p)).

Next, we use these values to standardize the distribution using the formula z = (x - np) / sqrt(np(1-p)), where x is the number of adults who smoke in the survey (19). We can then use a standard normal distribution table or calculator to find the probability of getting 19 or fewer adults who currently smoke cigarettes.

The probability is approximately 0.905, which corresponds to option A.