Question

Internet Browsers Recently, the top web browser had 51.28% of the market. In a random sample of 250 people, what is the probability that fewer than 118 did not use the top web browser? Round the final answer to at least 4 decimal places and intermediate e value calculations to 2 decimal places. P(X<118)

Answer 1

The question asks for the probability that less than 118 out of 250 people do not use the top web browser, which involves calculating a z-score and referencing the standard normal distribution with previous steps including finding the mean and standard deviation for the binomial distribution.

Step-by-step explanation:

The question relates to the probability of a specific outcome occurring in a given random sample based on binomial distribution. Given that the top internet browser has 51.28% market share, the complement (those not using the top browser) would be 48.72%. For a sample size of 250, we can calculate the probability that fewer than 118 people do not use the top web browser using the normal approximation to the binomial, with the sample proportion (p') calculated as 1 - 0.5128 = 0.4872.

To find the probability P(X<118), where X represents the number of people not using the top browser:

1. Calculate the mean (μ) of the distribution: μ = n * p'
2. Calculate the standard deviation (σ) of the distribution: σ = sqrt(n * p' * (1 - p'))
3. Convert 118 to a z-score and use the standard normal distribution to find the related probability.

Intermediate and final answers should be rounded appropriately as per request.