Answer to Question #129228 in Statistics and Probability for manoj b

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.