Answered: An elevator has a placard stating that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

An elevator has a placard stating that the maximum capacity is 1360 lb—8 passengers. So, 8 adult male passengers can have a mean weight of up to 1360/8=170 pounds. If the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 170 lb. (Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 32 lb.)

Does this elevator appear to be safe?

1. The probability the elevator is overloaded is____

2. Does the elevator appear safe? (choose the best answer below)

A - No, 8 randomly selected people will never be under wright

B - Yes, 8 randomly selected adult male passengers will always be under the weight limit.

C - No, there is a good chance that 8 randomly selected adult male passengers will exceed the elevator capacity.

D - Yes, there is a good chance that 8 randomly selected people will not exceed the elevator capacity.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

From the above question we observe that,

mean , $μ$ =180 lb

standard deviation, $σ$ =32 lb.

We use the z-score value to interpret the answer.

$Z = \frac{x - μ}{σ}$

Where,

$μ = m e a n o f t h e p o p u l a t i o n σ = s \tan d a r d d e v i a t i o n$

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