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Solnce55 [7]
3 years ago
15

Please help with this question thanksm

Mathematics
1 answer:
cluponka [151]3 years ago
5 0

Answer: a) 1/64

Step-by-step explanation:

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A simple random sample of size nequals10 is obtained from a population with muequals68 and sigmaequals15. ​(a) What must be true
valentina_108 [34]

Answer:

(a) The distribution of the sample mean (\bar x) is <em>N</em> (68, 4.74²).

(b) The value of P(\bar X is 0.7642.

(c) The value of P(\bar X\geq 69.1) is 0.3670.

Step-by-step explanation:

A random sample of size <em>n</em> = 10 is selected from a population.

Let the population be made up of the random variable <em>X</em>.

The mean and standard deviation of <em>X</em> are:

\mu=68\\\sigma=15

(a)

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Since the sample selected is not large, i.e. <em>n</em> = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.

Then, the mean of the distribution of the sample mean is given by,

\mu_{\bar x}=\mu=68

And the standard deviation of the distribution of the sample mean is given by,

\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{10}}=4.74

Thus, the distribution of the sample mean (\bar x) is <em>N</em> (68, 4.74²).

(b)

Compute the value of P(\bar X as follows:

P(\bar X

                    =P(Z

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

Thus, the value of P(\bar X is 0.7642.

(c)

Compute the value of P(\bar X\geq 69.1) as follows:

Apply continuity correction as follows:

P(\bar X\geq 69.1)=P(\bar X> 69.1+0.5)

                    =P(\bar X>69.6)

                    =P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{69.6-68}{4.74})

                    =P(Z>0.34)\\=1-P(Z

Thus, the value of P(\bar X\geq 69.1) is 0.3670.

7 0
3 years ago
Find all solutions by factoring.<br> c? + 13c + 40 = 0
Karolina [17]

Answer: c = -5, -8

Step-by-step explanation:

c^2 +13c+40=0

(c+5)(c+8)=40

c = -5, -8

3 0
3 years ago
Which fraction is closer to 0 than 1​
scoundrel [369]

Answer:

5/12

Step-by-step explanation:

Since 1/2 is the same distance from zero and one, we can use it to judge whether a fraction is closer to 0 or 1.

Since 5/8 is greater than 4/8 which is 1/2, it is closer to 1.

Since 8/10 is greater than 5/10 which is 1/2, it is closer to 1.

Since 5/12 is less than 6/12 which is 1/2, it is closer to 0.

So our answer is C. 5/12

3 0
3 years ago
Solve this proportion pls<br><br> <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%20%2B%203%7D%7B4%7D" id="TexFormula1" title="\fr
emmasim [6.3K]

\bf \cfrac{x+3}{4}=\cfrac{7}{8}\implies 8(x+3)=4(7)\implies 8x+24=28\implies 8x=4 \\\\\\ x=\cfrac{4}{8}\implies x=\cfrac{1}{2}

8 0
3 years ago
Read 2 more answers
What is the circumference of the following circle?<br> 3cm
Paul [167]

Answer:

here is the answer

Step-by-step explanation:

circumferential of a circle = 2π r

2x22/7x 3

18.85

pls mark me as brain list answer

5 0
2 years ago
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