Answer: 0.1854
Step-by-step explanation:
Given : Suppose that a particular candidate for public office is in fact favored by 48% of all registered voters in the district.
Let 
be the sample proportion of voters in the district favored a particular candidate for public office .
A polling organization will take a random sample of n=500 voters .
Then, the probability that p will be greater than 0.5, causing the polling organization to incorrectly predict the result of the upcoming election :
![P(\hat{p}>0.5)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.5-0.48}{\sqrt{\dfrac{0.48(0.52)}{500}}})\\\\=P(z>0.8951)\ \ [\because\ z=(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\=1-P(z\leq0.8951)\ \ [\because\ P(Z>z)=1-P(Z\leq z)]\\\\ = 1-0.8146=0.1854](https://tex.z-dn.net/?f=P%28%5Chat%7Bp%7D%3E0.5%29%3DP%28%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%3E%5Cdfrac%7B0.5-0.48%7D%7B%5Csqrt%7B%5Cdfrac%7B0.48%280.52%29%7D%7B500%7D%7D%7D%29%5C%5C%5C%5C%3DP%28z%3E0.8951%29%5C%20%5C%20%5B%5Cbecause%5C%20z%3D%28%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5D%5C%5C%5C%5C%3D1-P%28z%5Cleq0.8951%29%5C%20%5C%20%5B%5Cbecause%5C%20P%28Z%3Ez%29%3D1-P%28Z%5Cleq%20z%29%5D%5C%5C%5C%5C%20%3D%201-0.8146%3D0.1854)
∴ Required probability = 0.1854
Answer: $0.14 per ounce
Step-by-step explanation:
There are 28.5 ounces of shampoo in the shampoo bottle and the cost of the whole bottle is $3.99.
The cost per ounces will therefore be:
= Cost of bottle / Number of ounces
= 3.99 / 28.5
= $0.14 per ounce
Division expression: 7 divided by 9
5x - 2. Just combine like terms, and distribute the + to the second term.
Answer: 3 people ordered soup.
Step-by-step explanation:
Let x be the number of people ordered salad and y be the number of people ordered soup.
As per given,
x=2y (i)
7.50x+6.25y= 63.75 (ii)
Substitute value of c =2y in (ii) , we get
7.50(2y)+6.25y= 63.75
⇒ 15y+6.25y = 63.75
⇒21.25y = 63.75
⇒ y= 3 [divide both sides by 21.25]
Then, x= 2(3) =6
So 6 people ordered salad and 3 people ordered soup.
