Ask question

Ask question

All categories

2 years ago

12

50 11th graders were asked to choose which of 6 options the school’s color should be. The table below shows the number of studen

ts who chose each color. Use the data to answer the questions.
Color Frequency
Red 10
Blue 7
Orange 5
Black 6
Silver 8
Gold 14

1. Jake wants to make a relative frequency bar graph from these data, with the vertical axis marked off in percentages, from 0 up to 30 percent. What should be the height of the bar for blue?

2. Kate wants to make a relative frequency bar graph from these data, with the vertical axis marked off in percentages, from 0 up to 30 percent. What should be the height of the bar for red?

1 answer:

Rzqust [24]2 years ago

7 0

The height of the blue bar should be 14%.
The height of the red bar should be 20%.

You might be interested in

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls invol

bagirrra123 [75]

Answer:

a) 0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b) 0.118 = 11.8% probability that exactly 4 of the calls involve a fax message

c) 0.904 = 90.4% probability that at least 4 of the calls involve a fax message

d) 0.786 = 78.6% probability that more than 4 of the calls involve a fax message

Step-by-step explanation:

For each call, there are only two possible outcomes. Either it involves a fax message, or it does not. The probability of a call involving a fax message is independent of other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

25% of the incoming calls involve fax messages

This means that $p = 0.25$

25 incoming calls.

This means that $n = 25$

a. What is the probability that at most 4 of the calls involve a fax message?

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$ .

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001$

$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.001 + 0.006 + 0.025 + 0.064 + 0.118 = 0.214$

0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b. What is the probability that exactly 4 of the calls involve a fax message?

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

0.118 = 11.8% probability that exactly 4 of the calls involve a fax message.

c. What is the probability that at least 4 of the calls involve a fax message?

Either less than 4 calls involve fax messages, or at least 4 do. The sum of the probabilities of these events is 1. So

$P(X < 4) + P(X \geq 4) = 1$

We want $P(X \geq 4)$ . Then

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001$

$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.096 = 0.904$

0.904 = 90.4% probability that at least 4 of the calls involve a fax message.

d. What is the probability that more than 4 of the calls involve a fax message?

Very similar to c.

$P(X \leq 4) + P(X > 4) = 1$

From a), $P(X \leq 4) = 0.214)$

Then

$P(X > 4) = 1 - 0.214 = 0.786$

0.786 = 78.6% probability that more than 4 of the calls involve a fax message

8 0

2 years ago

A coach gives her players the option of running around their field twice or around their entire stadium once. The following diag

Elodia [21]

Get a call to me when I can do it on Saturday

7 0

2 years ago

A tank can contain 40 gallons of gas, but it is not completely full. How much gas is in the tank if 6.5% of the tank is empty?

Katena32 [7]

37.4 Gallons of gas should be your answer! Hope i helped!

6 0

2 years ago

Read 2 more answers

Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon combines an amount of the two cereals in a single bowl of mi

almond37 [142]

Answer:

There are 4 ounces of Fiber X cereal in the mix

Step-by-step explanation:

Lets n be the amount of ounces of Fiber X in the mix. Since there are a total of 12 ounces in the mix, then, on terms of n, there are 12-n ounces of Fiber Max on it.

Since 65% of the mix is Fiber, then there are 12*0.65 = 7.8 ounces of Fiber. We can also obtain this value if we take the proportions of Fiber in each cereal of the mix (in terms of n), so that we can obtain the true value of n

we have

7.8 = n *0.55 + (12-n)*0.7 = 0.55n + 8.4 -0.7 n = 8.4-0.15n

Therefore

0.15 n = 0.6

n = 0.6/0.15 = 4

As a consecuence, there are 4 ouces of Fiber X cereal in the mix.

6 0

2 years ago

Ralph bought a computer monitor with an area of 384 square inches. The length of the monitor is six times the quantity of five l

Alenkasestr [34]

Draw the picture and label the
width = w
The length of the monitor is six times the quantity of five less than half its width:
length = 6(w/2-5)
length = 3w-30
Area = (length)*(width)
384=(3w-30)*(w)
384=3w^2-30w
Answer:
the dimensions of the monitor in terms of its width is:
384=3w^2-30w

7 0

2 years ago