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
