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Alex17521 [72]
3 years ago
9

"is it appropriate to use the normal approximation for the sampling distribution of"

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
5 0

Answer: Normal approximation can be used for discrete sampling distributions, such as Binomial distribution and Poisson distribution if certain conditions are met.

Step-by-step explanation: We will give conditions under which the Binomial and Poisson distribitions, which are discrete, can be approximated by the Normal distribution. This procedure is called normal approximation.

1. Binomial distribution: Let the sampling distribution be the binomial distribution B(n,p), where n is the number of trials and p is the probability of success. It can be approximated by the Normal distribution with the mean of np and the variance of np(1-p), denoted by N(np,np(1-p)) if the following condition is met:

n>9\left(\frac{1-p}{p}\right)\text{ and } n>9\left(\frac{p}{1-p}\right)

2. Poisson distribution: Let the sampling distribution be the Poisson distribution P(\lambda) where \lambda is its mean. It can be approximated by the Normal distribution with the mean \lambda and the variance \lambda, denoted by N(\lambda,\lambda) when \lambda is large enough, say \lambda>1000 (however, different sources may give different lower value for \lambda but the greater it is, the better the approximation).

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I really need help! Please, please, PLEASE do not give me a link.
MArishka [77]

Answer:

7 fiction and 23 non- fiction

Step-by-step explanation:

The number of non-fiction read was 5 less than 4 times the number of fiction books.

Assume fiction books are x.

An equation representing this would be:

x + (4x - 5) = 30

5x - 5 = 30

5x = 30 + 5

x = 35 / 5

x = 7 fiction books

Non-fiction books:

= 4x - 5

= 4 * 7 - 5

= 23 non - fiction books

3 0
2 years ago
Read 2 more answers
A survey showed that 35% of the students prefer plain white milk over chocolate milk. If the school has 1200 students. How many
vodomira [7]

Answer:

The number of students who prefer chocolate milk is 780 .

Step-by-step explanation:

Given as :

The total number of students in the school = 1200

The percentage of students who prefer plain white milk = 35 %

Let the number of students who prefer chocolate milk = x

Now, ∵ The percentage of students who prefer plain white milk = 35 %

∴ The percentage of students who prefer chocolate milk = 100 % - 35 % = 65%

So , As The number of  students who prefer chocolate milk = x

Or, 65 % of total number of students in school = x

So, x = \frac{65}{100} × 1200

or, x = \frac{65\times 1200 }{100}

∴  x = 780

So, the number of students who prefer chocolate milk = x = 780

And  students who prefer plain white milk = 1200 - x = 1200 - 780 = 420

Hence, The number of students who prefer chocolate milk is 780 . Answer

4 0
3 years ago
Five and one half less than 3 times a number
Rama09 [41]

3x - 5 1/2      is the expression


5 0
3 years ago
Last Wednesday, a random sample of 24 students were surveyed to find how long it takes to walk from the Fretwell Building to the
Ray Of Light [21]

Answer:

E

Step-by-step explanation:

Solution:-

- We are to investigate the confidence interval of 95% for the population mean of walking times from Fretwell Building to the college of education building.

- The survey team took a sample of size n = 24 students and obtained the following results:

                Sample mean ( x^ ) = 12.3 mins

                Sample standard deviation ( s ) = 3.2 mins

- The sample taken was random and independent. We can assume normality of the sample.

- First we compute the critical value for the statistics.

- The z-distribution is a function of two inputs as follows:

  • Significance Level  ( α / 2 ) = ( 1 - CI ) / 2 = 0.05/2 = 0.025

Compute: z-critical = z_0.025 = +/- 1.96

- The confidence interval for the population mean ( u ) of  walking times is given below:

                      [ x^ - z-critical*s / √n  ,   x^ + z-critical*s / √n  ]

Answer:        [ 12.3 - 1.96*3.2 / √24  ,  12.3 + 1.96*3.2 / √24  ]

                   

3 0
3 years ago
If h(x) = (f o g)(x) and h(x) = ∛7x+1, find f(x) and g(x)
Mariana [72]
There's more than one way to combine them really
but an obvious one will be

\bf \begin{array}{llll}
h(x)&=&(f\circ g)(x)\\\\
&&\sqrt[3]{7x+1}\\\\
&&\sqrt[3]{g(x)}\leftarrow 
\begin{array}{llll}
f(x)=\sqrt[3]{x }\\\\
g(x)=7x+1
\end{array}
\end{array}\\\\
-----------------------------\\\\
(f\circ g)(x)\iff f[\quad g(x)\quad ]=\sqrt[3]{g(x)}\implies  f[\quad g(x)\quad ]=\sqrt[3]{7x+1}
7 0
3 years ago
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