Question

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what she found. Type of Crust Number Sold Thin crust 291 Thick crust 234 Stuffed crust 180 Pan style 270 Based on this information, of the next pizzas she sells 3500, how many should she expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answer 1

Answer:

The owner is expected to sell 840 thick crust pizzas.

Step-by-step explanation:

The Mancini's Pizzeria sells four types of pizza crust:

Thin crust, Thick crust, Stuffed crust and Pan style.

The number of pizzas sold of each type in the past week are:

Thin crust:       291

Thick crust:     234

Stuffed crust:   180

Pan style:         270

_______________

Total:                975

Compute the proportion of each type of pizzas sold.

Proportion of Thin crust $=\frac{291}{975}=0.2985$

Proportion of Thick crust $=\frac{234}{975}=0.24$

Proportion of Stuffed crust $=\frac{180}{975}=0.1846$

Proportion of Pan style $=\frac{270}{975}=0.2769$

Now let the random variable X be defined as the number of thick crust pizzas sold.

The number of pizzas sold, n = 3500.

The proportion of thick crust pizzas, p = 0.24.

The random variable X follows a Binomial distribution with parameters n = 3500 and p = 0.24.

The expected value of a binomial random variable is:

$E(X)=np$

Compute the expected number of thick crust pizzas sold as follows:

$E(X)=np$

         $=3500\times 0.24\\=840$

Thus, the owner is expected to sell 840 thick crust pizzas.