Respuesta :
Answer:
Option A - 60
Step-by-step explanation:
Given : On a very hot summer day, 5 percent of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism.
To find : What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?
Solution :
Applying Binomial distribution,
[tex]P(x)=^nC_x p^x q^{n-x}[/tex]
Here, p is the success p=5%=0.05
q is the failure [tex]q= 1-p=1-0.05=0.95[/tex]
n is the number of selection n=10
The probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent i.e. x=0
Substitute the values,
[tex]P(0)=^{10}C_0 (0.05)^0 (0.95)^{10-0}[/tex]
[tex]P(0)=\frac{10!}{10!0!}\times1\times (0.95)^{10}[/tex]
[tex]P(0)=1\times 0.5987[/tex]
[tex]P(0)=0.5987[/tex]
[tex]P(0)\approx 0.60[/tex]
i.e. 60%.
Therefore, Option A is correct.
