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PolarNik [594]
2 years ago
11

Picky Polls asked 1600 third-year college students if they still had their original major. According to the colleges, 50% of all

third-year college students still had their original major. Picky Polls got less than 800 students who said they still had their original major. How likely is this result? Assume the normal model applies here. You may use your calculator or reference the z tables when working with normal models.

Mathematics
1 answer:
Reptile [31]2 years ago
7 0

Answer:

The probability that less than 800 students who said they still had their original major is 0.50 or 50%.

Step-by-step explanation:

Let the random variable <em>X</em> be described as the number of third-year college students if they still had their original major.

The probability of the random variable <em>X</em> is, P (X) = <em>p</em> = 0.50.

The sample selected consisted of <em>n</em> = 1600 third-year college students.

The random variable <em>X </em>thus follows Binomial distribution with parameters n = 1600 and p = 0.50.

X\sim Bin(1600, 0.50)

As the sample size is large, i.e.<em>n</em> > 30, and the probability of success is closer to 0.50,  Normal approximation can be used to approximate the binomial distribution.

The mean of <em>X</em> is:

\mu_{x}=np=1600\times0.50=800\\

The standard deviation of <em>X</em> is:

\sigma_{x}=\sqrt{np(1-p}=\sqrt{1600\times0.50(1-0.50)}=20

It is provided that Picky Polls got less than 800 students who said they still had their original major.

Then the probability of this event is:

P(X

**Use the <em>z</em>-table for the probability.

Thus, the probability that less than 800 students who said they still had their original major is 0.50.

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If a person starts investing $100 per month starting at age 21, and that money earns a 5% return every year, how much will this
aalyn [17]

The formula for calculating compound interest with yearly contributions is:

Balance = X*(1 + Y)^n + Z((1 + Y)^(n + 1) - (1 + Y)/Y)

where the balance is the money earned after n years invested

Y is the interest rate as a fraction

Z is the yearly contribution

X is the starting investment

Therefore the calculation for this example is:

Balance = 1200*(1 + 0.05)^48 + 1200((1.05)^49 - (1.05)/05)

= $249,393.5


8 0
3 years ago
Read 2 more answers
*Will mark Brainliest (10 points)*<br><br> Please explain, thanks!
MAVERICK [17]
Standard form Ax + By = C
so
<span>(y - y1) = m(x - x1)
</span>given (5, -7) and m = -1/5
so
y + 7 = -1/5(x - 5)
-5y - 35 = x - 5
x + 5y = -30

answer
d. x + 5y = -30
5 0
3 years ago
What are the domain and range of the inequality y &lt; sqrt x+3+1
love history [14]

Given:

The inequality is:

y

To find:

The domain and range of the given inequality.

Solution:

We have,

y

The related equation is:

y=\sqrt{x+3}+1

This equation is defined if:

x+3\geq 0

x\geq -3

In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.

So, the domain of the given inequality is x>-3.

We know that,

\sqrt{x+3}\geq 0

\sqrt{x+3}+1\geq 0+1

y\geq 1

The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.

So, the domain of the given inequality is y>1.

Therefore, the correct option is A.

3 0
3 years ago
(10
Anni [7]

Given:

The matrix multiplication

\begin{bmatrix}4&5&6\\1&2&3\end{bmatrix}\begin{bmatrix}10\\20\\30\end{bmatrix}

To find:

The order of resulting matrix.

Solution:

We know that, if order of first matrix is m_1\times n_1 and the order of second matrix is m_2\times n_2, then the order of these two matrices is m_1\times n_2.

We have,

\begin{bmatrix}4&5&6\\1&2&3\end{bmatrix}\begin{bmatrix}10\\20\\30\end{bmatrix}

Here, the order of first matrix is 2\times 3 and the order of the second matrix is 3\times 1. So, the order of the second matrix is 2\times 1. It is also written are 2 by 1.

Therefore, the correct option is A.

6 0
3 years ago
Read 2 more answers
1) Q: A: Factor x2 + 8x + 16 A) (x + 4)2 B) (x - 4)2 C) (x + 8)(x + 2) D) (x + 2)(x - 8)
luda_lava [24]

Answer:

(x+4)^2  Choice A

Step-by-step explanation:

x^2 + 8x + 16

what 2 numbers multiply together to give you 16 and add together to give you 8

1*16 = 16   1+16 = 17  no

2*8 = 16   2+8 = 10  no

4*4 = 16  4+4 = 8  yes


(x+4) (x+4)

(x+4)^2

8 0
3 years ago
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