Answer to Question #134743 in Statistics and Probability for Margaret

Question

The number of times the AI algorithm is successful at detecting fake news is normally distributed with a sample mean of 900 and the sample standard deviation of 30. Assume a sample osize of 100 was used.
What is the 99% confidence interval estimate for the population mean?
1. (862.6636 ; 937.3364)
2. (864.2155 ; 935.7845)
3. (892.1208 ; 907;8792)
4. (892.9062 ; 907;0938)
5. (892.2600 ; 907.7400)

Answer 1

We need to construct the 99% confidence interval for the population mean 

μ. The following information is provided:

sample mean $\overline{X}=900\\s=30\\N=100$

since sample size is larger and normally distributed , we use Z confidence interval .

The critical value for α=0.01 is $z_c = z_{1-\alpha/2} = 2.576$

.The corresponding confidence interval is computed as shown below:

$\begin{array}{ccl} CI= \displaystyle \left( \bar X - z_c \times \frac{\sigma}{\sqrt{n}}, \bar X + z_c \times \frac{\sigma}{\sqrt{n}} \right) \\ \\ \displaystyle= \left( 900 - 2.576 \frac{30}{\sqrt{100}} , 900 + 2.576 \frac{30}{\sqrt{100}} \right) \\ \\ = (892.26, 907.74) \end{array} ​$

Answer: option 5