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A bridge on a small, rural road is designed to hold 10 cars when it is full and its maximum continuous weight that the bridge is designed to hold is 39,000 pounds. Assume that the average American car weighs 3750 pounds and that American cars' weights have a standard deviation of 200 pounds. If the bridge is fully loaded with 10 cars, what is the probability that it will be overloaded

Respuesta :

Answer:

0.0089

Step-by-step explanation:

given,

mean of average american Car (μ) = 3750 pounds

standard deviation (σ) = 200 pound

n = 10

sample average = [tex]\bar{x} = \dfrac{39000}{10}[/tex]

                           = 3900 pounds

[tex]\mu_{\bar{x}} = 3750\ ponds[/tex]

[tex]\sigma_{\bar{x}} = \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\sigma_{\bar{x}} = \dfrac{200}{\sqrt{10}}[/tex]

[tex]\sigma_{\bar{x}} = 63.25[/tex]

[tex]P(\bar{x}>3900) = 1 - P(\bar{x}<3900)[/tex]

= [tex]1 - P[\dfrac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}<\dfrac{3900-3750}{63.25}][/tex]

= 1 - P(Z<2.37)

using z- table

= 1 - 0.9911

= 0.0089

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