The weight of luggage that a randomly selected airline passenger brings onto a flight has a mean of 35 lbs and a standard deviation of 6 lbs. If a flight has 80 passengers, within what range would the average weight of their luggage fall with 95% certainty?
http://davidmlane.com/hyperstat/z_table.html
To calculate it yourself:
95% = mean ± Z (SEm)
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (±.025) and its Z score. Insert data into above equation.
To find the range within which the average weight of the luggage for 80 passengers would fall with 95% certainty, we can use the concept of confidence intervals.
A confidence interval is a range of values within which we can estimate the population parameter (in this case, the average weight of luggage) with a certain level of confidence.
Since the sample size is large (80 passengers) and we are given the standard deviation of the population (6 lbs), we can use the z-distribution and the formula for confidence intervals.
The formula for a confidence interval of a population mean is given by:
CI = X̄ ± z * (σ / √n)
Where:
CI = Confidence interval
X̄ = Sample mean
z = Z-score corresponding to the desired level of confidence
σ = Population standard deviation
n = Sample size
In this case:
X̄ = 35 lbs (mean weight of luggage)
z = Z-score corresponding to a 95% confidence level, which is approximately 1.96 (look it up in a Z-table)
σ = 6 lbs (standard deviation of luggage weight)
n = 80 (number of passengers)
Plugging the values into the formula, we get:
CI = 35 ± 1.96 * (6 / √80)
Calculating this expression, we find:
CI ≈ 35 ± 1.96 * 0.6708
CI ≈ 35 ± 1.3156
Therefore, the range within which the average weight of luggage for 80 passengers would fall with 95% certainty is approximately:
(35 - 1.3156) lbs to (35 + 1.3156) lbs
This simplifies to approximately:
33.6844 lbs to 36.3156 lbs
So, with 95% certainty, the average weight of the luggage for 80 passengers would fall within the range of 33.6844 lbs to 36.3156 lbs.