Answer to Question #193061 in Statistics and Probability for Dhiraj Ramji Singh

Question

The maximum weight that an elevator in an apartment complex can accommodate is 800kg.

The average adult weight be about 70 kgs with a variance of 200. What is the probability

that the lift safely reaches the ground when there are 10 adults in the lift?

Answer 1

Given mean= 70

variance = 200

hence mean for 10 adults = 10(70)= 700

variance for 10 adults = 10(200)= 2000

therefore standard deviation sd = $\sqrt{2000}$ = 44.72

If the weight > 800 kg causes the elevator to "unsafely" reach the ground, then we can find the upper tail of our normal distribution:

P(Weight of 10 adults > 800 kg).

$Z-score =\frac{ (X-mu)}{SD} = \frac{(800-700)}{44.72} = 2.24$

Hence P( Z <2.24), using z table we get 0.9875 or 98.75%

Hence it is safe to reach the ground when there are 10 adults in the lift.