Question

NO LINKS!! Please help me with this probability question 3a​

Answer 1

b) 26%

Explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

`\large\boxed{X \sim\text{N}(\mu,\sigma^2)}`

Given:

`\textsf{Mean}\;\mu=3550`

`\textsf{Standard deviation}\:\sigma=870`

Therefore, if the weights of the cars passing over the bridge are normally distributed:

`\boxed{X \sim\text{N}(3550,870^2)}`

where X is the weight of the car.

To find the approximate probability that the weight of a randomly-selected car passing over the bridge is less than 3000 pounds, find
`\text{P}(X < 3000)`.

Calculator input for "normal cumulative distribution function (cdf)":

• Upper bound: x = 3000
• Lower bound: x = –9999...
• μ = 3550
• σ = 870

`\implies \text{P}=0.2636333503`

`\implies \text{P}=26\%`

Therefore, the approximate probability that the weight of a randomly-selected car passing over the bridge is less than 3000 pounds is 26%.