A carnival ride has cars that each hold 4 44 adult passengers. The weights of the passengers for this ride are normally distributed with a mean of 65 kg 65kg65, start text, k, g, end text and a standard deviation of 12 kg 12kg12, start text, k, g, end text. Assume that the weights of passengers are independent from each other. Let T = T=T, equals the total weight of 4 44 randomly selected adult passengers for this ride. Find the probability that the total weight exceeds 290 kg 290kg290, start text, k, g, end text. You may round your answer to two decimal places.

The probability that the total weight exceeds 290 Kg is 0.23 and this can be determined by using the normal distribution formula.

Given :

The mean of T is given by the following calculation:

The standard deviation of T is given by the following calculation:

To determine the probability P(T > 290) use the formula of normal distribution which is given below:

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.

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