Can someone please answer 1 for me? Whoever can answer gets brainliest

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 N (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 n = 10 is selected from a population.

Let the population be made up of the random variable X.

The mean and standard deviation of X are:

$\mu=68\\\sigma=15$

(a)

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 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. n = 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 N (68, 4.74²).

(b)

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

$P(\bar X$

$=P(Z$

*Use a z-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

A rectangle measures 2 4/ 5 inches by 1 1/ 5 inches. What is its area?

AlexFokin [52]

[ Answer ]

$\boxed{3\frac{9}{25} }$

[ Explanation ]

Area Of Rectangle: Length * Width

2 4/5 * 1 1/5

=======================

Convert Fractions Into Mixed Numbers:

2 4/5 = 14/5

1 1/5 = 6/5

Multiply Across:

14 * 6

5 * 5

= 84/ 25

Simplify:

3 9/25

$\boxed{[ \ Eclipsed \ ]}$

4 0

3 years ago

Find the common difference for the given sequence shown. 56,49,42,35

ddd [48]

Answer:

-7

Step-by-step explanation:

let the first term be a

thus, a=56

common difference d= U2-U1 = 49-56= -7

4 0

3 years ago

How to write the inverse of 3x+4y=12 in f^-1 (x)?

mojhsa [17]

3x+4y=12

4y=12-3x

y=(12-3x)/4 <---------- This is f(x)

---------------------

3x+4y=12

3x=12-4y

x=(12-4y)/3

Therefore:

f⁻¹(x)=(12-4x)/3

=[4(3-x)]/3

8 0

2 years ago

A 15ftX20ft room has a 6ft diameter circular rug in it. How much of the flood is not covered by the rug?

Luda [366]

Answer:

There are 271.74 ft^2 not covered by the rug

The percentage not covered by the rug is 90.58%

Step-by-step explanation:

step 1

Find out the area of the room

The area of the rectangular room is

$A=(15)(20)=300\ ft^2$