Question

On the average, hotel guests who take elevators weigh about 150 pounds with an SD of about 35 pounds. An engineer is designing a large elevator for a convention hotel, to lift 50 such people. If she designs it to lift 4 tons, the chance it will be overloaded by a random group of 50 people is about . Explain briefly.

Answer 1

Answer:

Probability is only 2.5%

This is arrived based on the central limit theorem that sample mean follows a normal distribution for large samples randomly drawn.

Step-by-step explanation:

Given that on the average, hotel guests who take elevators weigh about 150 pounds with an SD of about 35 pounds.

An engineer is designing a large elevator for a convention hotel, to lift 50 such people.

Maximum capacity = 4 tons =8000 pounds

= 160 pounds/man

If average of 50 people exceeds 160 pounds then it would be overloaded.

Mean of the sample follows a normal with mean = 150 and std error = $\frac{35}{\sqrt{50-1} } \\=5$

Required probability

= $P(\bar x >160)\\= P(Z>2)\\\\=0.0250$

Probability is only 2.5%

This is arrived based on the central limit theorem that sample mean follows a normal distribution for large samples randomly drawn.