Question

Based on a sample of 30 randomly selected years, a 90% confidence interval for the mean annual precipitation in one city is from 40.3 inches to 43.7 inches. Find the margin of error. A) 3.4 inches B) There is not enough information to find the margin of error. C) 1.7 inches D) 0.51

Answer 1

To find the margin of error from the confidence interval (40.3 inches to 43.7 inches), calculate the midpoint and subtract the lower bound. The margin of error is therefore 1.7 inches.

Step-by-step explanation:

The question asks how to find the margin of error from a given confidence interval for the mean annual precipitation in one city. The confidence interval provided is from 40.3 inches to 43.7 inches. To find the margin of error, we calculate the distance from the midpoint of this interval to either endpoint because the margin of error is the maximum amount that the sample estimate can differ from the population parameter while still being within the confidence interval.

First, find the midpoint of the interval (which is the sample mean), then subtract the lower bound of the interval from the midpoint (or vice versa with the upper bound), as follows:

Midpoint (Mean) = (40.3 + 43.7) / 2 = 42 inches

Margin of Error = 43.7 - 42 = 1.7 inches

Therefore, the correct answer is C) 1.7 inches.

Answer 2

C) 1.7 inches

Step-by-step explanation:

According to the situation, the solution of the margin of error is as follows

The Margin of error is

= 1 ÷ 2 × length of the confidence interval

where,

length of the confidence interval is from 40.3 inches to 43.7 inches

Now putting these values to the formula above

So, the margin of error is

= 1 ÷ 2 × (40.3 inches - 43.7 inches )

= 1.7 inches