He mean weight of luggage checked by a random selected tourist-class passenger yingbetween two cities on a certain airline is 40 lb, and the standard deviation is 10 lb. The meanand standard deviation for a business-class passenger and 30 lb and 6 lb, respectively. Supposethere are 12 business-class passengers and 50 tourist-class passengers on a particular ight. Find the mean and standard deviation of total luggage weight.

The mean total luggage weight is 2,360 lb.

The standard deviation of total luggage weight is 505.16 lb.

Step-by-step explanation:

Let the random variables be defined as follows:

X = weight of luggage checked by tourist-class passengers

Y = weight of luggage checked by business-class passengers

The mean and standard deviation of random variable X are:

The mean and standard deviation of random variable Y are:

In the flight there were 12 business-class passengers and 50 tourist-class passengers.

Te equation representing the total luggage weight is:

T = 50 X + 12 Y

Compute the mean total luggage weight as follows:

Thus, the mean total luggage weight is 2,360 lb.

The two random variables X and Y are independent. This is because the two random variables describes values from two different population, one being weight of tourist class passenger and the other being business class passengers.

So, the covariance between X and Y is 0.

Compute the standard deviation of total luggage weight as follows:

Thus, the standard deviation of total luggage weight is 505.16 lb.

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