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Minchanka [31]
3 years ago
10

So far a total of 48 tickets have been sold for the school play for a total revenue of $220. How many student tickets have been

sold? Set up and solve a system of equations to solve the problem.
Adult = $7
Student=$3
Mathematics
1 answer:
Advocard [28]3 years ago
6 0
Let x be the number of adult tickets and y be the number of student tickets.

From the first sentence we can set up both equations:

1) x + y = 48
2) 7x + 3y = 220

Rearrange #1 to isolate x:
x = 48 - y

Sub that into #2 and solve for y to get your answer:
7(48 - y) + 3y = 220
336 - 7y + 3y = 220
-4y = -116
y = 29

29 student tickets were sold.
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Answer:

a) P(X

And we can find this probability using the normal standard distribution or excel and we got:

P(z

b) P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

P(z>3.78)=1-P(Z

c) z=0.674

And if we solve for a we got

a=43 +0.674*4.5=46.033

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.  

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".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(43,4.5)  

Where \mu=43 and \sigma=4.5

Part a

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the normal standard distribution or excel and we got:

P(z

Part b

P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

P(z>3.78)=1-P(Z

Part c

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=43 +0.674*4.5=46.033

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.  

8 0
3 years ago
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