Respuesta :
Answer:
0
Step-by-step explanation:
Let X to be a random variable that looks a binomial distribution which denoted the number of employees out of the 281 who earn the prevailing minimum wage or less
The sample size n = 281
The population parameter p = 5% = 0.05
Using normal approximation for the mean.
[tex]\mu = np[/tex]
[tex]\mu = 281\times 0.05[/tex]
[tex]\mu = 14.05[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{np(1-p)}[/tex]
[tex]\sigma = \sqrt{281 \times 0.05(1-0.05)}[/tex]
[tex]\sigma = \sqrt{281 \times 0.05(0.95)}[/tex]
[tex]\sigma = \sqrt{13.3475}[/tex]
[tex]\sigma =3.6534[/tex]
By using continuity correction; the sample mean x is:
x = 30 - 0.5
x = 29.5
The z statistic test can now be as follows:
[tex]Z = \dfrac{x-\mu}{\sigma}[/tex]
[tex]Z = \dfrac{29.5-14.05}{3.6534}[/tex]
[tex]Z = \dfrac{15.45}{3.6534}[/tex]
Z = 4.23
Thus, the probability that company A will get a discount is
P(X ≥ 30) = P(Z >4.23)
= 1 - P(Z < 4.23)
By using the Excel function for the z score 4.23 i.e. "=1 - NORMSDIST(4.23)" we get;
= 0.0000
The discount value is "0".
Let X be a random variable that shows how many employees out of 281 earn the prevailing minimum wage or less.
X does have a binomial distribution with parameters [tex]n = 281 \ \ and\ \ p = 0.05[/tex]:
Since [tex]np \ \ and\ \ n(1-p)[/tex] are greater than 5, X does have a normal distribution of parameters when using the normal approximation.
[tex]\to \mu= np=281 \times 0.05= 14.05[/tex]
Calculating the standard deviation:
[tex]\to \sigma=\sqrt{np(1-p)}\\\\[/tex]
[tex]= \sqrt{281 \times 0.05 (1-0.05)}\\\\=\sqrt{281 \times 0.05 \times 0.95}\\\\ =\sqrt{14.05 \times 0.95}\\\\ =\sqrt{13.3475}\\\\=3.653[/tex]
Continuity correction is required in this case. The z-score for [tex]X = 30-0.5 = 29.5[/tex]:
[tex]\to z= \frac{X- \mu}{\sigma}[/tex]
[tex]=\frac{29.5-14.05}{3.653}\\\\=\frac{15.45}{3.653}\\\\=4.2294\\\\[/tex]
The likelihood that Company Its will receive the discount:
[tex]\to P(X\geq 30)=P(z>4.229)=0.0000117\approx \ 0.0000[/tex]
Therefore, the final answer is "0".
Learn more about the discount:
brainly.com/question/16051609
