SOLUTION: 4. An elevator has a placard stating that the maximum capacity is 3800 lb — 26 passengers. So, 26 adult male passengers can have a mean weight of up to 3800/26=146 pounds. Ass
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-> SOLUTION: 4. An elevator has a placard stating that the maximum capacity is 3800 lb — 26 passengers. So, 26 adult male passengers can have a mean weight of up to 3800/26=146 pounds. Ass
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Question 1199258: 4. An elevator has a placard stating that the maximum capacity is 3800 lb — 26 passengers. So, 26 adult male passengers can have a mean weight of up to 3800/26=146 pounds. Assume that weights of males are normally distributed with a mean of 185 lb and a standard deviation of 31 lb.
a. Find the probability that 1 randomly selected adult male has a weight greater than 146 lb.
b. Find the probability that a sample of 26 randomly selected adult males has a mean weight greater than 146 lb.
You can put this solution on YOUR website! sample size is 26
maximum capacity is 3800 pounds
maximum mean weight of 26 passengers is 3800 / 26 = 146 pounds.
weight of males is normally distributed with a mean of 185 pounds and a standard deviation of 31 pounds.
z-score formula is z = (x - m) / s
x is the weight of an individual or the mean weight of a number of individuals.
m is the mean weight to test against.
s the standard deviation if one individual is tested or the standard error if the mean of a number of individuals is tested.
when checking the weight of an individual, use the standard deviation of the population of men.
z = (x - m) / s becomes z = (146 - 185) / 31
x is the weight you want to test against the mean = 146
m is the mean of the weight of men = 185
s is the standard deviation of the weight of men = 31
solve for z to get z = -1.25806 rounded to 5 decimal places.
since you want to know the probability that a man weighs more than 146 pounds, you are looking for the area to the right of that z-score.
you can use a z-score calculator to find that.
i used the ti-84 plus calculator.
using my ti-84 plus, i get the area to the right of a z-score of -1.25806 = .8958 rounded to 4 decimal places.
the online calculator does the same thing, only rounds differently form some values.
the result of using that calculator with the z-score is shown below.
the result of using that calculator with the raw score is shown below.
when you are looking at the mean of a sample of a number of individuals, you use the standard error.
the standard error is equal to the standard deviation / the square root of the sample size.
in this problem, the sample size is 26 individuals whose mean weight is 185 and whose standard deviation is 31.
the standard error is equal to 31 / sqrt(26) = 6.0796 rounded to 4 decimal places.
z = (146 - 185) / 6.0796 in this case.
146 is the weight you are testing against.
185 is the meaan weight of men.
6.0796 is the standard error.
the z-score is equal to -6.4149 rounded to 4 decimal places.
the probability of the mean of all men being greater than 146 pounds is equal to .99999...... when i use my ti-84 plus calculator.
that's very very close to 100%.
the online calculator shows 1 which is equal to 100%.
the result of using that calculator with the z-score is shown below.
the result of using that calculator with the raw score is shown below.
