A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there
are 12,600 sedans in Anytown, how many motorcycles are there?
1 answer:
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Answer:
a)
And we can find this probability with this difference:
And using the norma standard distribution or excel we got:
b)
And using the complement rule we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference:
And using the norma standard distribution or excel we got:
Part b
For this case we want this probability:
And we can use the z score and we got:
And using the complement rule we got:
The <em><u>correct answer</u></em> is:
3 inches.
Explanation:
We will use the Rational Roots Theorem to solve this.
First we can divide both sides of the equation by 4 in order to simplify it:
In order to solve this, we want the polynomial set equal to 0. To do this, subtract 105 from both sides:
The Rational Roots Theorem says that if p/q is a root of the polynomial, then p is a factor of the constant term and q is a factor of the leading coefficient. The constant term is -105. Drawing a factor tree, we find that the factors of this number are 1, -1, 3, -3, 5, -5, 7, -5, 15, -15, 21, -21. The leading coefficient is 1; its only factor is 1. This means p/q must be a whole number, and can be any of the factors of 105.
Using synthetic division, we try 1 in the box:
<u>1 |</u> 1 -18 80 -105
_______<u> 1</u>__<u> -17</u>___<u>63</u>__
1 -17 63 -42
Since there is a remainder, this is not a root. Trying -1,
<u>-1 |</u> 1 -18 80 -105
_______<u>-1</u>__<u> 19 </u>_<u>-99</u>_
1 -19 99 -204
This is not a root; in fact, it shows us that none of the negatives will be a factor, as the absolute values increase as we complete the synthetic division.
Trying 3,
3 | 1 -18 80 -105
________<u>3</u>__<u>-45</u>___<u>105</u>_
1 -15 35 0
Since there is no remainder, 3 is a root, and is the answer we are looking for.