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24. Ninety-four percent of NCSU transfers feel that their college adequately prepared them to handle upper-division coursework at their transfer university. We randomly survey 14 NCSU transfers. We are interested in the number that feel that their college adequately prepared them to handle upper division coursework at their transfer university. Find the probability that more than half felt that they were prepa

Sagot :

Answer:

The answer is "[tex]0.99999340657 \sim 1[/tex]".

Step-by-step explanation:

[tex]Sucess \ probability \ (p) = 94\% \ or\ 0.94\\\\Sample\ numbers\ n = 14\\[/tex]  

Using formula:

[tex]P(X=r)= ^n C_r \times p^r \times (1-p)^{n-r}[/tex]

 Let

[tex]\to r=8,9,10,11,12,13 \ or\ 14\\\\[/tex]

Substituting the value for all r:

 [tex]P(X=8)= 0.00008540547\\\\P(X=9)= 0.00089201264\\\\P(X=10)= 0.00698743233\\\\P(X=11)= 0.03980719025\\\\P(X=12)= 0.15591149513\\\\P(X=13)= 0.37578668058\\\\P(X=14)= 0.42052319017\\[/tex]

Therefore,

[tex]P(X>7)= P(X=8)+P(X=9)+....P(X=14)\\\\= 0.99999340657 \sim 1.[/tex]

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