Respuesta :
The probability that the total weight exceeds 290 Kg is 0.23 and this can be determined by using the normal distribution formula.
Given :
- A carnival ride has cars that each hold 4 adult passengers.
- The weights of the passengers for this ride are normally distributed with a mean of 65 kg.
- The standard deviation of 12 kg.
The mean of T is given by the following calculation:
[tex]\mu_T = 4\times 65[/tex]
[tex]\mu_T = 260[/tex]
The standard deviation of T is given by the following calculation:
[tex]\sigma^2_T=12^2+12^2+12^2+12^2[/tex]
[tex]\sigma_T = \sqrt{4\times 12^2}[/tex]
[tex]\sigma_T = 24[/tex]
To determine the probability P(T > 290) use the formula of normal distribution which is given below:
[tex]\rm P(T>290) = \int\limits^{9999}_{290} {\dfrac{e^{\frac{-(x-260)^2}{24}}}{24\sqrt{2\pi} } \, dx[/tex]
By simplifying the above integration the value of the probability is given by:
P(T > 290) = 0.23
So, the probability that the total weight exceeds 290 Kg is 0.23.
For more information, refer to the link given below:
https://brainly.com/question/23044118
