Question

Which probability distribution table corresponds with this frequency distribution table?

Answer 1

Answer:

Table 2

Step-by-step explanation:

The given frequency distribution table is

X  :   1           2           3            4           5

f   :   11          1            2           4           2

The sum of frequencies is

$\sum f=11+1+2+4+2=20$

The formula for probability is

$P_i=\frac{f_i}{\sum f}$

where, $f_i$ is frequency and $\sum f$ in the sum of frequencies.

For X=1,

$P_1=\frac{11}{20}=0.55$

For X=2,

$P_2=\frac{1}{20}=0.05$

For X=3,

$P_3=\frac{2}{20}=0.1$

For X=4,

$P_4=\frac{4}{20}=0.2$

For X=5,

$P_5=\frac{2}{20}=0.1$

The probability distribution table corresponds with the given frequency distribution table is

X  :   1           2           3            4           5

P   :   0.55    0.05    0.1          0.2       0.1

Therefore, the correct option is 2.

Answer 2

The only probability distribution table that corresponds with the frequency distribution table is; Second table

From the given frequency distribution table, let's find the sum of the given frequencies. Thus;

Σf = 11 + 1 + 2 + 4 + 2

Σf = 20

Now,the probability for each value of x will be;

P_x = f_x/Σf

Where f_x represents the frequency of the given value of x.

Thus;

P_1 = 11/20

P_1 = 0.55

P_2 = 1/20

P_2 = 0.05

P_3 = 2/20

P_3 = 0.1

P_4 = 4/20

P_4 = 0.2

P_5 = 2/20

P_5 = 0.1

Looking at the tables in the options, in conclusion the only tables that have their P value corresponding with those we got for each value of x is Option B which is the second table.

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