A shop sells a chicken pasta dish. The main ingredients are pasta, chicken and sauce. Each...

A shop sells a chicken pasta dish. The main ingredients are pasta, chicken and sauce. Each chicken pasta dish contains 250grams of pasta and 100gram of chicken. The price of a pack of 500 grams of pasta is normally distributed with mean $1 and variance $0.4. The price of a pack of 200 grams of chicken is normally distributed with mean $2 and variance $0.8. The sauce in each chicken pasta dish costs $0.5.

What distribution does the total cost of one chicken pasta dish follow? [6 Marks]

Expert Solution

Let X1: Price of a pack of 500 grams of pasta.

The price of a pack of 500 grams of pasta is normally distributed with mean $1 and variance $0.4

Let X2: Price of a pack of 200 grams of chicken.

The price of a pack of 200 grams of chicken is normally distributed with mean $2 and variance $0.8

Each chicken dish contains 250 grams of pasta and 100 grams of chicken. That is half of each pack of pasta and chicken.

The total cost of one chicken pasta dish is 1/2 X1 + 1/2 X2 + 0.5

0.5 is the cost of sauce.

1/2 X1 follows a normal distribution with mean 1/2 * 1and variance (1/2)² * 0.4 that is mean 0.5 and variance 0.1

Similarly, 1/2 X2 follows a normal distribution with mean 1/2 * 2 and variance (1/2)² * 0.8 that is mean 1 and variance 0.2

The distribution of the total cost of one chicken pasta dish follows a normal distribution with mean 2 and variance 0.3

orchestra answered 2 years ago

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