Question

2. Practice with Statistics. (12 pts) (Feel free to use a calculator (or spreadsheet) to
add/divide/etc, but please don’t use built-in statistical functions.)

You measure the lengths of 14 objects in a box, and get the following results (in cm): 1; 3; 3; 4;
4; 5; 5; 5; 5; 7; 7; 7; 8; 9

a) What is the probability that an object chosen at random from this box has length 4 cm? (Here and
below, assume equal probability for selecting any one object)

b) What’s the average length <L> (also called the expectation value of length) of the objects?

c) What is the probability that an object chosen at random from the box has length = <L> ?

d) What is the average value of the square of the lengths, <L2>?

e) Use your results to find the standard deviation s of lengths of objects in this box

f) What is the probability that the length of an object chosen randomly from this box is in the
range <L> +/- s? (Given what you know about stand. deviation, does this seem reasonable?)

Answer 1

Given  

Length (cm)	No. of objects
1	1
3	2
4	2
5	4
7	3
8	1
9	1

(a)

no. of objects with length 4cm = 2

Total no. of objects = 14

probability =P  

​

(b)  

Probability of selecting any i object =  

  

(C)   

we got that  

but we don't have object with this length but if consider  

then probabilty  

highest probability in given sample.

(d)

  

(e) Standered daviation