A fitness company is building a 20-story high-rise. Architects
building the high-rise know that women working for the company have
weights that are normally distributed with a mean of 143 lb and a
standard deviation of 29 lb, and men working for the company have
weights that are normally distributed with a mean of 167 lb and a
standard deviation or 25 lb. You need to design an elevator that
will safely carry 18 people. Assuming a worst case scenario of 18
male passengers, find the maximum total allowable weight if we want
to a 0.98 probability that this maximum will not be exceeded when
18 males are randomly selected.
The maximum weight for the elevator is ______________ pounds.
Solution,
Given that,
mean = = 167 lb (men)
standard deviation = = 25 lb
n = 18
= = 167 lb
= / n = 25 / 18 = 5.89 lb
Using standard normal table,
P(Z > z) = 0.98
= 1 - P(Z < z) = 0.98
= P(Z < z ) = 1 - 0.98
= P(Z < z ) = 0.02
= P(Z < -2.054) = 0.02
z = -2.054
Using z-score formula
= z * +
= -2.054 * 5.89 + 167
= 154.90
The maximum weight for the elevator is 155 pounds.
A fitness company is building a 20-story high-rise. Architects building the high-rise know that women working...
A fitness company is building a 20-story high-rise. Architects building the high-rise know that women working for the company have weights that are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men working for the company have weights that are normally distributed with a mean of 184 lb and a standard deviation of 23 lb. You need to design an elevator that will safely carry 15 people. Assuming a worst case scenario...
bue in a hours, 24 minutes. Due Thu 01/24/2019 12:15 pm A fitness company is building a 20-story high-rise. Architects building the high- rise know that women working for the company have weights that are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men working for the company have weights that are normally distributed with a mean of 165 lb and a standard deviation or 24 lb. You need to design an...
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