Suppose that a survey is taken of a sample of portuguese parents with at least one child under the age of 20 living at home. the parents are asked to report the number of days per week, , in which they have family dinner at home. identify which of the tables are valid probability models for . 0 1 2 3 4 5 6 7 (x) 0.100.10 0.050.05 0.100.10 0.200.20 00 0.100.10 0.200.20 0.250.25 0 1 2 3 4 5 6 7 (x) 0.1250.125 0.1250.125 0.1250.125 0.1250.125 0.1250.125 0.1250.125 0.1250.125 0.1250.125 0 1 2 3 4 5 6 7 (x) 0.100.10 0.150.15 0.200.20 0.250.25 0.300.30 0.350.35 0.400.40 0.450.45 0 1 2 3 4 5 6 7 (x) 00 1010 1010 1010 1010 1010 2525 2525 0 1 2 3 4 5 6 7 (x) −0.50−0.50 0.200.20 0.200.20 0.200.20 0.200.20 0.200.20 0.200.20 0.200.20

Step-by-step explanation:

For a valid probability model for X.

For X=0,1,2,3,4,5,6,7

\small 0\leq P(X)\leq 1 (as P(X) is Probability ; Probability can only between 0 and 1).

On this Count ;

these options are not valid ; 3 and 5

X            0   1   2   3   4    5   6  7

P(X)        0   l0 l0   l0   l0 l0   25 25

X          0         I        2       3       4       5          6          7

P(X)  -0.50  0.20  0.20 0.20 0.20  0.20    0.20   0.20      

And also for a valid probability model for X.  

\small \sum_{X=0}^{7}P(X) =1  

For option 1:

\small \sum_{X=0}^{7}P(X) =0.125+0.125+0.125+0.125+0.125+ 0.125+0.125+0.125=1

Option1 satisfies both the conditions

Option 2 :

\small \sum_{X=0}^{7}P(X) =0.10+0.05+0.10+0.20+0+ 0.10+0.20+0.25=1

Option 2 satisfies both the conditions

For Option 4,

\small \sum_{X=0}^{7}P(X) =0.10+0.15+0.20+0.25+0.30+ 0.35+0.40+0.45=2.2\small \sum_{X=0}^{7}P(X) =2.2\neq 1

Hence option 4 does not satisfy condition 2

SO , the correct answer is option 1 and 2

X     0     1    2       3     4    5     6     7

PX) 0.125 0.125 0.125 O.125 0.125 0.125 0.125 0.123

X     0     1    2       3     4    5     6     7

PX) 0.10   0.05 0.10    0.20   0    0.10 0.20  0.25

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

it’s supposed to be -4+45=41

step-by-step explanation: