The weight of adult males are normally distributed with a mean of 78kg and a sta

Question

The weight of adult males are normally distributed with a mean of 78kg and a standard deviation of 12 kg. Use this information to answer

parts (1) to (3)

1)What is the probability that one randomly selected adult male will weigh more than 85 kg?

2)What is the probability that 10 randomly selected adult males will have a mean weight of more than 85kg?

3An elevator at a fitness center had a maximum allowable weight of 850kg. If 10 randomly selected male cram into the elevator, what is the probability that the elevator will be over the maximum allowable weight?

Explanation / Answer

1)

mean = 78 , std. deviation = 12

By normal distribution formula,

z = ( x - mean) / ( s / sqrt(n))

= ( 85 - 78) / ( 12 / sqrt(1))

= 0.58

Now. we need to find p( z > 0.58)

p(x > 85) = p(z > 0.58) = 0.2798

2)

mean = 78 , std. deviation = 12

By normal distribution formula,

z = ( x - mean) / ( s / sqrt(n))

= ( 85 - 78) / ( 12 / sqrt(10))

= 1.84

Now. we need to find p( z > 1.84)

p(x > 85) = p(z > 1.84) = 0.0324

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