An elevator has a placard stating that the maximum capacity is 1610 lb---10 passengers. So, 10 adult male passengers can have a mean weight of up to1610 divided by 10 = 161 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than161lb. (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 35 lb.)Does this elevator appear to be safe?The probability the elevator is overloaded is?(Round to four decimal places as needed.)
Accepted Solution
A:
Answer:[tex]\mu = 165[/tex][tex]\sigma = 35[/tex]We are supposed to find the probability that it is overloaded because they have a mean weight greater than 161 lb.n = 10 males P(X>161)Formula : [tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [tex]z=\frac{161-165}{\frac{35}{\sqrt{10}}}[/tex] [tex]z=-0.3614[/tex]Refer the z table P(z<−0.3614)=0.6406P(x>161)=1-P(x<161)=1-P(z<−0.3614)=1-0.6406=0.3594The probability the elevator is overloaded is 0.3594The elevator is safe since the probability of overload is less than 0.5