Element X is a radioactive isotope such that every 25 years, its mass decreases by

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

The product of two consecutive even numbers is 224. What are these two numbers?

Stells [14]

Answer:

14 and 16

Step-by-step explanation:

They are the ONLY consecutive even numbers

And also

x and (x+2)

x(x+2)=224 ( product of a number and the consecutive of that number)

x ²+ 2x-224=0

(x+16)(x-14) =0

x=-16 or 14

In this case 14 and (14+2) 14 and 16

The integers are either 14 and 16 or -14 and -16.

4 0

2 years ago

Two lines are parallel if and only if their slopes are equal. Write two if-then statement that are implied by this thesis statem

Veronika [31]

If and only if (iff) statements are true if only both statements are true of both are false, its double implied.
Here are the implications:
If two lines are parallel then their slopes are equal.
If the slopes of two lines are equal then they are parallel.

5 0

3 years ago

What is the absolute value of -5/9

Finger [1]

Answer:

5/9

Step-by-step explanation:

In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:

Negative -> Positive

Positive -> Positive

Since we are working with a negative value, it will turn positive.

Best of Luck!

8 0

2 years ago

50,000+300+70+2 word form

Damm [24]

Fifty thousand three hundred seventy- two

5 0

2 years ago

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