Question

A study indicates that if eight people occupy the elevator, the probability distribution of the total...

A study indicates that if eight people occupy the elevator, the probability distribution of the total weight of the eight people is approximately normally distributed with a mean equal to 1,250 pounds and a standard deviation of 96 pounds.

What is the probability that the total weight of eight people exceeds 1,350 pounds? (Round your answers to four decimal places.)

What is the probability that the total weight of eight people exceeds 1,500 pounds? (Round your answer to four decimal places.)

Solution :

Given that ,

mean = = 1250

standard deviation = = 96

P(x >1350 ) = 1 - P(x <1350 )

= 1 - P[(x - ) / < (1350 -1250) /961]

= 1 - P(z <1.04 )

Using z table

= 1 - 0.8508

= 0.1492

probability= 0.1492

(b)

P(x >1500 ) = 1 - P(x <1500 )

= 1 - P[(x - ) / x < (1500 -1250) /96]

= 1 - P(z <2.60 )

Using z table

= 1 -0.9953

= 0.0047

probability= 0.0047

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