Respuesta :
Answer:
The probability is 0.6440
Step-by-step explanation:
The probability that x companies from the 100 in Country A have 3 or more female board directors follows a binomial distribution, so it is calculated as:
[tex]P(x)=100Cx*0.36^{x}*(1-0.36)^{100-x}[/tex]
Where 100 is the number of respondent and 0.36 is the probability that a company in country A have three or more female directors.
Additionally, 100Cx is calculated as:
[tex]100Cx=\frac{100!}{x!(100-x)!}[/tex]
Then, said that the sample will have between 29% and 38% of companies with three or more female board directors is equivalent to said that the sample will have between 29 and 38 companies with three or more female board directors.
So, the probability that the sample will have between 29% and 38% of companies in Country A that have three or more female board directors is calculated as:
P(29≤x≤38) = P(29) + P(30) + P(31) + ... + P(37) + P(38)
Where, for example, P(29) is:
[tex]P(29)=100C29*0.36^{29}*(1-0.36)^{100-29}=0.0292[/tex]
Finally, P(29≤x≤38) is equal to:
P(29≤x≤38) = 0.6440
