Question

The prices of pizzas can be described by a normal model with a mean of $12 and

a standard deviation of $3.

12. Draw the model showing the 68-95-99.7 Rule

13. Use the 68-95-99.7 Rule to estimate the proportion of pizzas with prices

between $12 and $18

14. Use the 68-95-99.7 Rule to estimate the proportion of pizzas with prices less

than $9

15. Use the 68-95-99.7 Rule to estimate the proportion of pizzas with prices more than $21

Answer 1

12.

Suppose, random variable X denotes price of pizza.

We know,

• One standard deviation interval about mean possesses 68% area.
• Two standard deviation interval about mean possesses 95% area.
• Three standard deviation interval about mean possesses 99.7% area.

So, the probability distribution model showing 68-95-99.7 rule is as follows.

In the diagram,

• The interval [9, 15] which is coloured in green contains 68% area.
• The interval [6, 18] which is coloured in green and blue contains 95% area.
• The interval [3, 21] which is coloured in green, blue and red contains 99.7% area

13.

From the diagram we can calculate the required probability as follows.

14.

From the diagram we can calculate the required probability as follows.

15.

From the diagram we can calculate the required probability as follows.