A simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard deviation of 34. Which of the following values is outside the 99% confidence interval for the population mean? Use the table to help you answer the question. Confidence Level 90 percent 95 percent 99 percent z to the ast th power -score 1 point 6 4 5 1 point 9 6 2 point 5 8 Remember, the margin of error, ME , can be determined using the formula ME is equal to the fraction with numerator z times s and denominator square root of n
Answer
A
the value of 154 because it is greater than 153 point 2
B
the value of 137 because it is greater than 136 point 5
C
the value of 135 because it is not greater than 136 point 5
D
the value of 138 because it is less than 153 point 2
Explanation
For a 99% confidence interval, use z = 2.58. The margin of error is 2.58 × 34 ÷ √85 ≈ 9.5, so the interval is about 146 − 9.5 to 146 + 9.5, or 136.5 to 155.5. The value 135 is below the interval, so choice D, “the value of 135,” is outside it; 154 is within the interval.
AI-written and checked against the verified answer.