Question 1132991
the average weight of males is 161 pounds with a standard deviation of 25 pounds.


that's your population if i understand it correctly.


you choose 8 men randomly from this population.


you want to know the probability that this sample of 8 men chosen randomly from the population will have a mean weight greater than 157 pounds.


mean of the sample is 161 pounds.
standard error of the sample of 8 males is 25 / sqrt(8).
z-score of the sample is z = (157 - 161) / (25 / sqrt(8)) = -4 / 8.838834765 = -.45254834
the probability of a sample of 8 men having a z-score greater than -.45254834 is equal to .6745629783.


your selection is D.
there's a good chance that 8 randomly selected males will exceed the elevator capacity.


visually, your distribution looks like this.


<img src = "http://theo.x10hosting.com/2019/011901.jpg" alt="$$$" >


the shaded area is the area under the normal distribution curve where the mean of your randomly selected 8 people is greater than 157.


note that the standard error is not the same as the standard deviation.
the standard deviation is for a sample of one person.
the standard error is for a sample of more than one person.
it is the standard deviation of the mean of that sample of more than one person.
the larger the sample size, the smaller the standard error.