Answer:
a
mean
variance ![\sigma^2 = 6](https://tex.z-dn.net/?f=%5Csigma%5E2%20%20%3D%206)
b
The binomial random variable x fall into this interval ranges from
- 5 to 5
c
Step-by-step explanation:
From the question we are told that
The sample size is ![n = 25](https://tex.z-dn.net/?f=n%20%20%3D%20%2025)
The percentage that look for gas stations and food outlets that are close to or visible from the highway is ![p = 0.40](https://tex.z-dn.net/?f=p%20%3D%20%200.40)
Generally the mean is mathematically represented as
![\mu = n * p](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%20n%20%2A%20%20p)
=> ![\mu = 0.40 * 25](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%200.40%20%2A%2025)
=> ![\mu = 10](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%2010)
The variance is mathematically represented as
![\sigma^2 = np(1- p )](https://tex.z-dn.net/?f=%5Csigma%5E2%20%20%3D%20%20np%281-%20p%20%29)
=> ![\sigma^2 = 25 * 0.40(1- 0.40 )](https://tex.z-dn.net/?f=%5Csigma%5E2%20%20%3D%20%2025%20%2A%200.40%281-%200.40%20%29)
=> ![\sigma^2 = 6](https://tex.z-dn.net/?f=%5Csigma%5E2%20%20%3D%206)
The standard deviation is mathematically evaluated as
![\sigma = \sqrt{\sigma^2}](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%20%5Csqrt%7B%5Csigma%5E2%7D)
![\sigma = \sqrt{6}](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%20%5Csqrt%7B6%7D)
![\sigma = 2.45](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%202.45)
The interval is evaluated as
![p\pm 2 \sigma](https://tex.z-dn.net/?f=p%5Cpm%20%202%20%5Csigma)
=> ![p - 2 \sigma\ \ \ , \ \ \ p + 2\sigma](https://tex.z-dn.net/?f=p%20-%20%202%20%5Csigma%5C%20%5C%20%5C%20%2C%20%5C%20%5C%20%5C%20%20p%20%2B%202%5Csigma)
=> ![0.40 - 2 *2.45\ \ \ , \ \ \ 0.40 + 2* 2.45](https://tex.z-dn.net/?f=0.40%20-%20%202%20%2A2.45%5C%20%5C%20%5C%20%2C%20%5C%20%5C%20%5C%20%200.40%20%2B%202%2A%202.45)
=> ![-4.5\ \ \ , \ \ \ 5.3](https://tex.z-dn.net/?f=-4.5%5C%20%5C%20%5C%20%2C%20%5C%20%5C%20%5C%205.3)
The binomial random variable x fall into this interval ranges from
- 5 to 5
Generally
![P(6 \le x \le 14) = P(\frac{ x - \mu }{\sigma } \le \frac{14 - 10}{{2.45}} ]-P[ \frac{ x - \mu }{\sigma } \le \frac{6 - 10}{2.45 } ]](https://tex.z-dn.net/?f=P%286%20%5Cle%20x%20%5Cle%2014%29%20%3D%20%20P%28%5Cfrac%7B%20x%20-%20%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%5Cle%20%20%5Cfrac%7B14%20-%2010%7D%7B%7B2.45%7D%7D%20%5D-P%5B%20%20%5Cfrac%7B%20x%20-%20%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%20%5Cle%20%5Cfrac%7B6%20-%2010%7D%7B2.45%20%7D%20%5D)
![P(6 \le x \le 14) = P(Z \le 1.63 ]-P[ Z \le -1.63 ]](https://tex.z-dn.net/?f=P%286%20%5Cle%20x%20%5Cle%2014%29%20%3D%20%20P%28Z%20%20%5Cle%201.63%20%5D-P%5B%20Z%20%20%5Cle%20-1.63%20%5D)
From the z-table
![P(Z > 1.63 ) = 0.051551](https://tex.z-dn.net/?f=P%28Z%20%20%3E%201.63%20%29%20%3D%200.051551)
And
![P(Z >- 1.63 ) =0.94845](https://tex.z-dn.net/?f=P%28Z%20%20%3E-%201.63%20%29%20%3D0.94845)
=>
=>
Answer:
I DO LOL
Step-by-step explanation:
sorry for caps
Answer:
![y=\frac{7-3x}{j}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B7-3x%7D%7Bj%7D)
Step-by-step explanation:
First, subtract 3x. This leaves you with jy=7-3x. Then, divide by j, leaving you with
.
Ms. Santos would be 29 years old
This is easy do you want me to explain it or give you a direct answer