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Delvig [45]
3 years ago
9

In June, Cory begins to save money for a video game and a TV he wants to buy in December.

Mathematics
1 answer:
bazaltina [42]3 years ago
5 0

Answer: B

Step-by-step explanation:

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Polly's Polls asked 1850 second-year college students if they still had their original major. According to the colleges, 65% of
suter [353]

Answer:

The probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424

Step-by-step explanation:

The variable that assigns the value 1 if a person had its original major and 0 otherwise is a Bernoulli variable with paramenter 0.65. Since she asked the question to 1850 people, then the number of students that will have their original major is a Binomial random variable with parameters n = 1850, p = 0.65.

Since the sample is large enough, we can use the Central Limit Theorem to approximate that random variable to a Normal random variable, which we will denote X.

The parameters of X are determined with the mean and standard deviation of the Binomal that we are approximating. The mean is np = 1850*0.65 = 1202.5, and the standard deviation is √np(1-p) = √(1202.5*0.35) = 20.5152.

We want to know the probability that X is between 0.64*1850 = 1184 and 0.66*1850 = 1221 (that is, the percentage is between 64 and 66). In order to calculate this, we standarize X so that we can work with a standard normal random variable W ≈ N(0,1). The standarization is obtained by substracting the mean from X and dividing the result by the standard deviation, in other words

W = \frac{X-\lambda}{\sigma} = \frac{X-1202.5}{20.5152}

The values of the cummulative function of the standard normal variable W, which we will denote \phi are tabulated and they can be found in the attached file.

Now, we are ready to compute the probability that X is between 1184 and 1221. Remember that, since the standard random variable is symmetric through 0, then \phi(-z) = 1-\phi(z) for each positive value z.

P(1184 < X < 1221) = P(\frac{1184-1202.5}{20.5152} < \frac{X-1202.5}{20.5152} < \frac{1221-1202.5}{20.5152})\\ = P(-0.9018 < W < 0.9018) = \phi(0.9018) - \phi(-0.9018) = \phi(0.9018)-(1-\phi(0.9018))\\ = 2\phi(0.9018)-1 = 2*0.8212-1 = 0.6424

Therefore, the probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424.

Download pdf
4 0
3 years ago
Last month, Ed ate 9 apples, 5 bananas, 4 peaches, and 7 oranges. Find the ratio bananas to the total number of fruit. Then expl
AlladinOne [14]

Answer:

Last month, Ed ate 9 apples, 5 bananas, 4 peaches, and 7 oranges. Find the ratio bananas to the total number of fruit. Then explain the meaning.

Step-by-step explanation:

first since there is 5 bananas it will be 5:_ and then the total so add up all the fruits

9+5+4+7=25 so

5:25

or

1:5

3 0
3 years ago
You cut a 54-inch rope into four pieces. Twoof the pieces are the same length, a thirdpiece is twice as long as each of the twoe
antiseptic1488 [7]

Let's use the variable x to represent the length of the first and second pieces.

If the third piece has twice the length of the first and second, its length is 2x.

If the fourth piece has half the length of the first and second, its length is 0.5*x.

Adding all four pieces and equating to 54 inches, we have:

\begin{gathered} x+x+2x+0.5x=54 \\ 4.5x=54 \\ x=\frac{54}{4.5} \\ x=12 \end{gathered}

So the length of each piece is:

12 inches, 12 inches, 24 inches and 6 inches.

5 0
1 year ago
What is the domain of the set of ordered pairs?<br> (8, -13); ( 0,-5); (4, -9); (-3,2)
UNO [17]

The domain is the input values, which are the x values.

The x values in the given pairs are: 8, 0,4,-3

The domain set is (-3, 0, 4, 8)

4 0
3 years ago
Read 2 more answers
A drawer contains 4 red socks, 5 white socks, and 6 blue socks. Without looking, you draw out a sock and then draw out a second
mezya [45]
The probability is (4/16) * (10/16) = 5/32
6 0
3 years ago
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