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Simora [160]
3 years ago
13

As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____. a. binomial distribution b.

Poisson distribution c. normal probability distribution d. hypergeometric distribution
Mathematics
1 answer:
kkurt [141]3 years ago
7 0

Answer:

c. normal probability distribution

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question:

By the Central Limit Theorem, it is a normal distribution, so option c.

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Two athletes practice for a marathon by running back and forth on a 11-mile course. They start running simultaneously, one at a
maks197457 [2]

Answer:

Faster runner speed: 11 mph

Slower runner speed: 9 mph

Distance from starting point: 9.9 miles

Step-by-step explanation:

Let the slower runner speed be: x

Faster runner speed: x+2

1 hour 6 minutes = 1.1 hours

Slower: 1.1(x) = 1.1x miles

Faster: 1.1(x+2) = 1.1x+2.2 miles

This means that the faster runner had gone 2.2 miles more than the slower runner.

1.1x + 2.2 > 11 miles (This is true as we know the faster runner is coming back from the 11 mile run)

1.1x > 11 - 2.2 miles

1.1x > 8.8 miles

x > 8.8 / 2.2 miles

x > 8 mph

1.1x < 11 miles (we know this is true as the slower runner has to have gone less than 11 miles as the faster runner met him on his way back)

x < 11 / 1.1 miles

x < 10 miles

8 < x < 10

Although x could be any number including decimal between 8 and 10, the obvious first answer would be 9. However we need to check if this answer is correct.

Slower runner distance to the end:

1.1(9) = 9.9 miles

11 - 9.9 = 1.1 miles

Faster runners distance from the end (when coming back)

1.1(9+2) = 1.1(11) = 12.1 miles

12.1 - 11 = 1.1 miles

The speeds 9 mph and 11 mph are now proven to be the right speeds. Using our equation before, we can figure out the distance from the starting point that they meet at. This is just how far the slower runner has gotten. So, 1.1(9) = 9.9 miles from the starting point

7 0
3 years ago
Here are the prices of five new pairs of hockey skates, in dollars: 59, 60, 65, 99, 175. The standard deviation is about $49. If
Phoenix [80]

Answer:

The standard deviation of the new data will be increased as compared to the previous standard deviation of the data.

Step-by-step explanation:

The prices are given to be : 59, 60, 65, 99, 175

Standard deviation = $49

Now, if we add or subtract any constant value to each of the terms then the standard deviation remains unchanged.

But, we add a new price in the given data that is $450

\text{New standard deviation = }\sqrt{\frac{\sum (\bar{x}-x_i)^2}{n}}\\\\\bar{x}\text{ is the mean of data after adding 450 and}\\x_i\text{ are the price values of the sample data}

Hence, Standard deviation is calculated to be 139.5

Therefore, the standard deviation of the new data will be increased as compared to the previous standard deviation of the data.

6 0
3 years ago
Read 2 more answers
12÷4×32+(4−2)5
Taya2010 [7]
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7 0
3 years ago
Robert climbed 755 steps in 12 1/2 minutes how many steps did he average per minute
Liula [17]
Basically, you have to do 755/12.5 That will give you your average per minute.
6 0
3 years ago
Read 2 more answers
What is the answer to question 10
Whitepunk [10]
He needs to earn ; 77.99-20= 57.99 dollars

so in one week there are 2 weekends; so he earns 6×3×2 = 36 dollars

so no of week = 57.99÷ 36= 1.6 weeks

so weeks are in natural no thus it will take him 2 weeks !!
8 0
3 years ago
Read 2 more answers
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