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garik1379 [7]
3 years ago
10

In a sample of 8 high school students, they spent an average of 28.8 hours each week doing sports with a sample standard deviati

on of 3.2 hours. Find the 95% confidence interval, assuming the times are normally distributed.

Mathematics
1 answer:
Alja [10]3 years ago
4 0

Answer:

26.12\:

Step-by-step explanation:

Since the population standard deviation \sigma is unknown, and the sample standard deviation s, must replace it, the t distribution  must be used for the confidence interval.

The sample size is n=8.

The degree of freedom is df=n-1, \implies df=8-1=7.

With 95% confidence level, the \alpha-level(significance level) is 5%.

Hence with 7 degrees of freedom, t_{\frac{\alpha}{2} }=2.365. (Read from the t-distribution table see attachment)

The 95% confidence interval can be found by using the formula:

\bar X-t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )\:.

The sample mean is \bar X=28.8 hours.

The sample sample standard deviation is s=3.2 hours.

We now substitute all these values into the formula to obtain:

28.8-2.365(\frac{3.2}{\sqrt{8} } )\:.

26.12\:

We are 95% confident that the population mean is between 26.12 and 31.48  hours.

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Degger [83]

Answer:

38 degrees

Step-by-step explanation:

this is an isosceles triangle, meaning that the base angles are congruent.

the total triangle is equal to 180

so the equation would be: x=180 - (71+71)

evaluate:

x=180-142

x=38 degrees

Hope this helps :)

5 0
2 years ago
A toy box contains eight green balls and four purple balls. Suppose you choose a ball at random and then replace it by putting i
dedylja [7]

Answer: C.  \dfrac{1}{3}

Step-by-step explanation:

Given: Box contains 8 green balls and 4 purple balls.

Total balls = 8+4 = 12

event 1 = first picking green ball

event 2 = second picking purple balls.

As first ball was replaced, that means both events are independent.

Probability that you have selected a green ball and then a purple ball = P(purple ball )

Formula for probability = \dfrac{\text{favorable outcomes}}{\text{total outcomes}}

Probability of selecting a purple ball (second pick)= \dfrac{4}{12}

=\dfrac{1}{3}

The required probability =\dfrac{1}{3}, so C is correct option.

3 0
3 years ago
Write the value of the expression 2^3/2^3
kiruha [24]

Answer:

1

Step-by-step explanation:

\frac{2^3}{2^3}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\=2^{3-3}\\2^{3-3}=1\\2^{3-3}\\\mathrm{Subtract\:the\:numbers:}\:3-3=0\\=2^0\\\mathrm{Apply\:rule}\:a^0=1,\:a\ne \:0\\=1

6 0
3 years ago
Help plz<br>6(2x - 11) + 15 = 3x + 12​
Ket [755]

Answer:

x = 7

Step-by-step explanation:

Lets do the brackets first,

6 × 2x = 12

6 × -11 = -66

------

Calculate the x constant:

12x - 3x = 9x

-------

Then the ones with no x:

-66 + 15 = -51

51 + 12 = 63

-------

Lastly, divide

63 ÷ 9 = 7

-------

Have a good day :)

3 0
2 years ago
Read 2 more answers
The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. Assuming that the food cos
JulijaS [17]

Answer:

The probability that a family spends less than $410 per month

P( X < 410) = 0.1151

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given mean of the population = 500 </em>

<em>Given standard deviation of the Population = 75</em>

Let 'X' be the variable in normal distribution

      Z = \frac{x-mean}{S.D}

<em>Given X = $410</em>

<em></em>Z = \frac{410-500}{75} = - 1.2<em></em>

<u><em>Step(ii):-</em></u>

The probability that a family spends less than $410 per month

P( X < 410) = P( Z < - 1.2 )

                  =  0.5 - A( -1.2)

                 = 0.5 - A(1.2)

                = 0.5 - 0.3849  ( ∵from normal table)

                = 0.1151

<u>Final answer:-</u>

The probability that a family spends less than $410 per month

P( X < 410) = 0.1151

6 0
3 years ago
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