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Luden [163]
3 years ago
10

2. 8.EE.1.2

Mathematics
1 answer:
Kryger [21]3 years ago
6 0
2 x 32 = 64
4 x 16 = 64
8 x 8 = 64
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4 years ago
At NC State University, 16.4% of the undergraduate classes have more than 50 students. If a random sample of 200 undergraduate c
Lena [83]

Answer:

We need to check the conditions in order to use the normal approximation.

np=200*0.164=32.8 \geq 10

n(1-p)=200*(1-0.164)=167.2 \geq 10

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

The mean is given by:

p =0.164

And the deviation is given by:

\sigma_{p}= \sqrt{\frac{0.164*(1-0.164)}{200}}= 0.0262

So then the correct options for this case are:

The sampling distribution will be approximately normal.

The mean of the sampling distribution will be 16.4%.

The standard deviation of the sampling distribution will be 0.0262.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=200, p=0.164)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

We need to check the conditions in order to use the normal approximation.

np=200*0.164=32.8 \geq 10

n(1-p)=200*(1-0.164)=167.2 \geq 10

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

The mean is given by:

p =0.164

And the deviation is given by:

\sigma_{p}= \sqrt{\frac{0.164*(1-0.164)}{200}}= 0.0262

So then the correct options for this case are:

The sampling distribution will be approximately normal.

The mean of the sampling distribution will be 16.4%.

The standard deviation of the sampling distribution will be 0.0262.

6 0
3 years ago
Each face of a small cube has a surface area of 0.25 square meters. A larger cube has edges that are six times as long as the ed
bezimeni [28]
First, you need to find the length of the smaller cubes side. To do this you would need to find the square root of 0.25. then you find the volume with the new found side length of the smaller cube by cubing the new side length and once you have your volume of smaller cube right it down.
Now you need to find the big cube volume by cubing its side length. Once you have found both of these volumes you subtract the smaller cube's volume from the bigger cube's volume to get the difference in size. Hope this helps
5 0
4 years ago
Read 2 more answers
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