Based on a sample of 32 randomly selected years,a 90% confidence interval for the mean annual precipitation in one city is from $119.1 \mathrm {~cm}$ to $125.9 \mathrm {~cm}$ .

Question

Quizplus · Accepted Answer

The confidence interval given is (11.2, 12.6).

The formula for the margin of error at 90% confidence level is

z* (population standard deviation/ sqrt(n))

Since the standard deviation is not given, we can use the range formula to estimate it. The range is

12.6 - 11.2 = 1.4

Assuming a normal distribution, 1.4/4 ~ 0.35 is the estimate of the standard deviation.

So, the margin of error is

1.645*0.35/sqrt(32) ~ 0.3

Thus, the estimate of the mean precipitation is

(11.2 + 12.6)/2 = 11.9

And the margin of error is +/- 0.3

Therefore, the best choice is C)3.4 cm as the margin of error is around 3.4 cm.

Based on a Sample of 32 Randomly Selected Years,a 90 119.1 cm119.1 \mathrm {~cm}119.1 cm

Based on a Sample of 32 Randomly Selected Years,a 90 $119.1 \mathrm {~cm}$