SOLUTION:
Step 1:
In this question, we are given the following;
The Society of Human Resource Managers reports that many resumes contain falsifications. Assuming that 55% of resumes contain falsifications, calculate the probability that among 11 randomly selected resumes, 9 of them contain falsifications.
Step 2:
The details of the solution are as follows:
This is an application of Binomial Distribution:
[tex]\begin{gathered} P^^\text{ \lparen X = x \rparen:} \\ ^nC_x(p)^x(q)^{n-x}\text{ , where p + q = 1} \end{gathered}[/tex][tex]Here,\text{ n = 11 , x = 9 , p = 55 \% = 0. 55 , q = 1 - 0. 55 = 0. 45}[/tex][tex]\begin{gathered} P\text{ \lparen X = 9 \rparen :} \\ 11\text{ C}_{9\text{ }}(\text{ 0. 55 \rparen}^9\text{ \lparen0. 45 \rparen}^{11-9} \end{gathered}[/tex][tex]\begin{gathered} P(\text{ X = 9 \rparen = 0.05129227} \\ P(\text{ X =9 \rparen}\approx\text{ 0. 051 \lparen correct to 3 decimal places\rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]0.051\text{ \lparen correct to 3 decimal places\rparen}[/tex]
