Snow Belt Airlines weighed the baggage of 100 passengers and found the mean weight to be 34.2 pounds with a standard deviation of 14 pounds.What is the 95% onfidence interval for the actual weight of the aggage ? Round Z to the nearest whole number)
A)20.0 - 48.2
B)32.8 - 35.6
C)31.4 - 37.0
D)0.0 - 50.0

Question

Quizplus · Accepted Answer

To find the 95% confidence interval, we use the formula:
CI = X̄ ± Z* (s/√n)
where X̄ is the sample mean, s is the sample standard deviation, n is the sample size, and Z* is the z-score corresponding to the desired level of confidence (95%). Since n > 30, we can use the standard normal distribution for Z*.

Z* for 95% confidence interval would be approximately 1.96 (rounded to the nearest whole number).
CI = 34.2 ± 1.96 * (14/√100)
CI = 34.2 ± 2.744
CI = (31.456, 37.944)

Therefore, the best choice is C, which shows the 95% confidence interval as 31.4 - 37.0.

Snow Belt Airlines Weighed the Baggage of 100 Passengers and Found