Solved Examples: Uniform Distribution

Prerequisite Topics
Uniform Distribution Calculators

For ACT Students
The ACT is a timed exam...$60$ questions for $60$ minutes
This implies that you have to solve each question in one minute.
Some questions will typically take less than a minute a solve.
Some questions will typically take more than a minute to solve.
The goal is to maximize your time. You use the time saved on those questions you solved in less than a minute, to solve the questions that will take more than a minute.
So, you should try to solve each question correctly and timely.
So, it is not just solving a question correctly, but solving it correctly on time.
Please ensure you attempt all ACT questions.
There is no negative penalty for any wrong answer.
Use the functions in your TI-84 Plus or TI-Nspire to solve some of the questions in order to save time.

For WASSCE Students
Any question labeled WASCCE is a question for the WASCCE General Mathematics
Any question labeled WASSCE-FM is a question for the WASSCE Further Mathematics/Elective Mathematics

For NSC Students
For the Questions:
Any space included in a number indicates a comma used to separate digits...separating multiples of three digits from behind.
Any comma included in a number indicates a decimal point.
For the Solutions:
Decimals are used appropriately rather than commas
Commas are used to separate digits appropriately.

Solve all questions.
Show all work.
You may use Possion Distribution Formulas or Poisson Distribution Tables or both.
However, if you are not asked to round your answers; then it is very necessary that you do not use Poisson Distribution Tables.
In other words, if you are not asked to round your answers; use Poisson Distribution Formulas.

(1.) Chloe wants to go skiing tomorrow, but only if there are 4 inches or more of new snow.
According to the weather report, any amount of new snow between 3 inches and 7 inches is equally likely.
The probability density curve for tomorrow's new snow depth is shown.
Find the probability that the new snow depth will be inches or more tomorrow.
Copy the graph, shade the appropriate area, and calculate its numerical value to find the probability.
The total area is 1.



(a.) Shade the area of the graph that represents the likelihood of 4 or more inches of new snow.



(b.) What is the probability that there will be 4 or more inches of new snow?

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(a.) The shaded area of the graph that represents the likelihood of 4 or more inches of new snow is: Option C.



(b.) From 3 to 7 is 4 parts
3 to 4 is one part
4 to 5 is one part
5 to 6 is one part
6 to 7 is one part
The total area is 1
This implies that each part is $\dfrac{1}{4} = 0.25$

We shaded 3 out of 4 parts
Therefore:

$ P(\ge 4\;\;inches\;\;of\;\;snow) \\[3ex] = 0.25 + 0.25 + 0.25 \\[3ex] = 0.75 $

(2.)

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(5.) Cosmas wants to go skiing tomorrow, but not unless there is between 2 and 5 inches of new snow.
According to the weather report, any amount of new snow between 1 inch and 6 inches is equally likely.
The probability density curve for tomorrow's new snow depth is shown.
Find the probability that the new snow depth will be within Cosmas' ideal range.
Copy the graph, shade the appropriate area, and calculate its numerical value to find the probability.
The total area is 1.



(a.) Shade the area of the graph that represents the likelihood of between 2 and 5 inches of new snow.



(b.) What is the probability that there will be 4 or more inches of new snow?

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(a.) The shaded area of the graph that represents the likelihood of between 2 and 5 inches of new snow is: Option D.



(b.) From 1 to 6 is 5 parts
1 to 2 is one part
2 to 3 is one part
3 to 4 is one part
4 to 5 is one part
5 to 6 is one part
The total area is 1
This implies that each part is $\dfrac{1}{5} = 0.2$

We shaded 3 out of 5 parts
Therefore:

$ P(between\;\;2\;\;and\;\;5\;\;inches\;\;of\;\;snow) \\[3ex] = 0.2(3) \\[3ex] = 0.6 $

(6.)

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