Question

A consulting agency reports that only \[30\%\] of a company's website users can successfully use a certain feature of the website. skeptical of this claim, one of the website developers takes a simple random sample of \[150\] of the company's approximately \[8000\] users and tests whether they can use the feature successfully. the developer finds that \[36\%\] of the sampled users use the feature successfully. assuming the agency's \[30\%\] claim is correct, what is the approximate probability that more than \[36\%\] of the sample would use the feature successfully? choose 1 answer: choose 1 answer:

Answer 1

To find the probability that more than 36% of the sample would use the feature, we calculate the z-score and use the normal distribution. The approximate probability is 3.42%.

Step-by-step explanation:

To solve this problem, we can use the normal distribution and the Central Limit Theorem. Since we have a sample size of 150 and want to find the probability that more than 36% of the sample would use the feature successfully, we need to calculate the z-score and find the corresponding probability. First, we calculate the standard error:

Standard Error = sqrt(p' * (1-p')/n) = sqrt(0.3 * 0.7/150) = 0.033

Next, we calculate the z-score using the given proportion of 0.36:

Z-score = (0.36 - 0.30) / 0.033 = 1.82

Finally, we find the probability of getting a z-score greater than 1.82 using a Z-table or a calculator. The approximate probability is 0.0342 or 3.42%.