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Sagot :
Answer: 0.6672
Explanation:
Let x be a random variable representing the weights of the cars. Since they are normally distributed and the population standard deviation is known, we would calculate the z score by applying the formula,
z = (x - μ)/σ
where
x is the sample size
μ = population mean
σ = population standard deviation
We want to find P(2800 < x < 4500)
From the information,
μ = 3550
σ = 870
For x = 2800,
z = (2800 - 3550)/870 = - 0.86
From the normal distribution table, the area under z = - 0.86 is 0.1949
For x = 4500,
z = (4500 - 3550)/870 = 1.09
From the normal distribution table, the area under z = 1.09 is 0.8621
Thus,
P(2800 < x < 4500) = 0.8621 - 0.1949 = 0.6672
the approximate probability that the weight of a randomly selected car passing over the bridge is between 2,800 and 4,500 pounds is 0.6672
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