Question

A researcher believes that 6% of females smoke cigarettes. If the researcher is correct, what is the probability that the proportion of smokers in a sample of 531 females would be greater than 4 % ? Round your answer to four decimal places.

Answer 1

To find the probability that the proportion of smokers in a sample of females would be greater than 4%, calculate the standard deviation and convert the threshold to a z-score using the normal distribution. The probability is approximately 0.9889.

Step-by-step explanation:

To find the probability that the proportion of smokers in a sample of 531 females would be greater than 4%, we need to use the normal distribution and standard deviation. Since the researcher believes the proportion of females who smoke is 6%, we can calculate the standard deviation as the square root of (6% * (1-6%) / 531).

Next, we need to convert the 4% threshold to a z-score by subtracting the mean (6%) from 4% and dividing by the standard deviation. Once we have the z-score, we can use a standard normal distribution table or a calculator to find the probability that a value is greater than that z-score. Rounding the answer to four decimal places, the probability is approximately 0.9889.