Which expression entered into a graphing calculator will return the probability

A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilogram

azamat

Answer:

(a) The variance decreases.

(b) The variance increases.

Step-by-step explanation:

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.

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

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

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

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The standard deviation of sample mean is inversely proportional to the sample size, n.

So, if n increases then the standard deviation will decrease and vice-versa.

(a)

The sample size is increased from 64 to 196.

As mentioned above, if the sample size is increased then the standard deviation will decrease.

So, on increasing the value of n from 64 to 196, the standard deviation of the sample mean will decrease.

The standard deviation of the sample mean for n = 64 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7$

The standard deviation of the sample mean for n = 196 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4$

The standard deviation of the sample mean decreased from 0.7 to 0.4 when n is increased from 64 to 196.

Hence, the variance also decreases.

(b)

If the sample size is decreased then the standard deviation will increase.

So, on decreasing the value of n from 784 to 49, the standard deviation of the sample mean will increase.

The standard deviation of the sample mean for n = 784 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2$

The standard deviation of the sample mean for n = 49 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8$

The standard deviation of the sample mean increased from 0.2 to 0.8 when n is decreased from 784 to 49.

Hence, the variance also increases.

6 0

2 years ago

Which graph represents a linear function? A coordinate plane is shown with a way line beginning along the x axis and continuing

Sliva [168]

-2-2 + 2 = 0(-2, 0)-1-1 + 2 = 1(-1, 1)00 + 2 = 2(0, 2)11 + 2 = 3(1, 3)22 + 2 = 4(2, 4)

5 0

2 years ago

Read 2 more answers

The probability that a random smoker will develop a sever lung condition during his or her lifetime is 0.3. we will choose a ran

postnew [5]

The mean is 36 and the standard deviation is 5.02.

The mean is given by
μ = np = 120*0.3 = 36.

The standard deviation is given by
σ = √(n*p*(1-p)) = √(120*0.3*0.7) = √25.2 = 5.02.

8 0

2 years ago

You and a friend have a hula hoop competition. you win 3 out of every 7 trials. your friend wins 5 more trials than you. how man

Ivenika [448]

Answer:

Total number of trials is 35.

Step-by-step explanation:

Given : Me and my friend have a hula hoop competition. I win 3 out of every 7 trials. My friend wins 5 more trials than me.

To find : How many trials are in the competition?

Solution :

Probability of my winning is 3 out of 7 trials $=\frac{3}{7}$

and probability of my friend's winning is $=1-\frac{3}{7}=\frac{4}{7}$

Let there be n numbers of trials.

Therefore, my score after n trials $=\frac{3n}{7}$

and my friend's score after n trials $=\frac{4n}{7}$

Now, the number of trials my friend won more than me is

$\frac{4n}{7}-\frac{3n}{7}=\frac{n}{7}$

We know, that my friend won 5 more trials than me so comparing the actual and given we get,

$\frac{n}{7}=5\\n=7\times5=35$

Therefore, total number of trials is 35.

We can also verify our answer by placing value of n,

After 35 trials I will win $\frac{3\times 35}{7}=15$ trials

and my friend will win $\frac{4\times 35}{7}=20$ trials.

Hence, my friend won 5 more trials than me.

3 0

2 years ago

The graph of F(x), shown below, has the same shape as the graph of G(x) = x2, but it is shifted up 3 units. What is its equation

Aliun [14]

For this case, the parent function is given by:
$G (x) = x ^ 2
$
Applying the following transformation we have:
Vertical displacement
Assume k> 0,
To graph y = f (x) + k, move the graph k units up.
We have then:
$F (x) = G (x) + 3

F (x) = x ^ 2 + 3$
Answer:
the equation of F (x) is given by:
$F (x) = x ^ 2 + 3$

5 0

2 years ago