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In: Statistics and Probability

A certain elevator has a maximum legal carrying capacity of 6000 pounds. Suppose that the population...

A certain elevator has a maximum legal carrying capacity of 6000 pounds. Suppose that the population of all people who ride this elevator have a mean weight of 160 pounds with a standard deviation of 25 pounds. If 35 of these people board the elevator, what is the probability that their combined weight will exceed 6000 pounds? Assume that the 35 people constitute a random sample from the population.

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Expert Solution

Solution :

Given that ,

mean = = 160

standard deviation = = 25

n = 35

= 6000 / 35 = 171

=   = 160

= / n = 25 / 35 = 4.23

P( > 171 ) = 1 - P( < 171 )

= 1 - P[( - ) / < ( 171 - 160 ) / 4.23 ]

= 1 - P(z < 2.60)

Using z table,    

= 1 - 0.9953

= 0.0047

orchestra answered 1 year ago
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