The capacity of an elevator is 12 people or 196S pounds. The capacity will be ex

Question

The capacity of an elevator is 12 people or 196S pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 1968/12-1M pounds. Suppose the people have vweiithb that are normally distributed with a mean of 168 lb and a standard deviation of 27 lb Find the probability that if a pervm w randomly selected. hit weight will he greater than 164 pounds The probability is approximately (Round to fow decimal places as needed.) Find the probability that 12 randomly selected people will have a mean that is greater than 164 pounds The probability it approximately, (Round to four decimal places as needed.) Does the elevator appear to have the correct weight limit? Why or why not? Yes. 12 randomly selected people will always be under the weight limit. No. ihere is a good chance that 12 randomly selected people will exceed the elevator capacity Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity No, 12 randomly selected people will never be under the weight

Explanation / Answer

mean = 168

standard deviation = 27

a) formula to be used = (x-mean)/standard deviation

p(x>164) =

For x = 164, z = (164 - 168) / 27 = - 0.14

Hence P(x > 164) = P(z > -0.14) = [total area] - [area to the left of -0.14]

1 - [area to the left of -0.14]

now from the z table we will take the value of z score = -0.14

    = 1 - 0.4443 = 0.5557

b) here n = 12

p(x>164) =

For x = 164, z = (164 - 168) /( 27/sqrt(12) = -0.51

Hence P(x > 164) = P(z > -0.51) = [total area] - [area to the left of -0.51]

1 - [area to the left of -0.51]

now from the z table we will take the value of z score = -0.51

    = 1 - 0.3050 = 0.695

c) yes there is a chance that they can be above the limit, option c is correct

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