If the average (arithmetic mean) of 10,20,30,40, and x is 60, what is the value of x

In a random sample of 20 NBA basketball games the mean number of points scored by the home team was 100.4 with a standard deviat

slava [35]

Answer:

The 95% confidence interval is $98.27 < \mu < 102.53$

This interval means that there 95% confidence that the true mean is within this interval

Yes i would agree with my friend because the lower and the upper limit 95% confidence interval for mean points scored at home is greater than 98 points

Step-by-step explanation:

From the question we are told that

The sample size is n = 20

The sample mean is $\mu = 100.4$

The standard deviation is $\sigma = 4.86$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{ \sqrt{n} }$

substituting values

$E = 1.96 * \frac{ 4.86 }{ \sqrt{20 } }$

$E = 2.13$

The 95% confidence interval is mathematically represented as

$\= x - E < \mu < \= x + E$

substituting values

$100.4 - 2.13 < \mu < 100.4 + 2.13$

$98.27 < \mu < 102.53$

5 0

4 years ago

Mrs. Wheeler prepares a list of 434343 US presidents, 313131 of whom served in the military. Then 888 students each select a pre

grigory [225]

Answer:

Probability of atleast one of the students(888) selecting a president with no service in the military reaches 1.

Step-by-step explanation:

Total Presidents in list = 434343

Military men to be president = 313131

Probability of selecting President who were also military men =

p = 313131/434343 = 0.72

Probability of selecting President who were not military men =

q = 1 - p = 1 - 0.72 = 0.28

Now; no of students who make a choice = 888

no. of Choices made resulting in success = x : {0, 1, 2, 3,............., 888 }

GIVEN CASE:

P(f) = Probability of atleast one student selecting a president with no service in military

This case fails when no one selects a president with no service in military, let us call it P(f').

P(f) = 1-P(f')

Calculating P(f'):

Let us define:

Failure = selecting a president with service in military , p = 0.72

Success = selecting a president with no service in military , q = 0.28

Using Binomial Theorem:

we have this case when n students make selections and x of them are successful.

$P(x) = nCx * q^{x} * p^{n-x}$

In case of f' , n = 888 and x = 0

$P(0) = 888 C 0 * (0.28)^{0} * 0.72^{888-0}$

$= (888!/(888-0)!) * (1) * (0.72)^{888}\\= (0.72)^{888}\\= 2.047655e-127\\$

Hence, P(f') = 2.047655e-127 (reaches 0)

Now: P(f) = 1 - P(f')

P(f) = 1 - 2.047655e-127 = 1

Hence Probability of atleast one of the students(888) selecting a president with no service in the military is 1.

7 0

3 years ago

Can someone help me out here please.

denis23 [38]

Answer:

im sorry but i have no clue what this is:(

Step-by-step explanation:

7 0

3 years ago

Perform the indicated operation.(3/a+2) + (4/a-5)

kipiarov [429]

Answer:

$\frac{7(a-1)}{(a+2)(a-5)}$

Step-by-step explanation:

To solve this operation we need to find the common multiple of both denominators and solve for a.

$\frac{3}{a+2} + \frac{4}{a-5} =\frac{3(a-5)+4(a+2)}{(a+2)(a-5)} =\frac{3a-15+4a+8}{(a+2)(a-5)} =\frac{7a-7}{(a+2)(a-5)} =\frac{7(a-1)}{(a+2)(a-5)}$

Thus, the solution is 7(a -1) / (a+2)(a-5)

8 0

4 years ago

An operational definition is used to ____ a hypothetical construct.

Alona [7]

An operational definition can both define and measure the hypothetical construct. The hypothetical construct is also called psychological construct is an explanatory variable which cannot be directly observed. It is also a tool to understand someone’s behavior. For example measuring you friend happiness.

8 0

4 years ago

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If the average (arithmetic mean) of 10,20,30,40, and x is 60, what is the value of x​

If the average (arithmetic mean) of 10,20,30,40, and x is 60, what is the value of x