Explain how to do 7.86×4.6

The National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time requir

Paha777 [63]

Answer:

95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean time = 5.15 years

$\sigma$ = sample standard deviation = 1.68 years

n = sample of college graduates = 4400

$\mu$ = population mean time

Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $5.15-1.96 \times {\frac{1.68}{\sqrt{4400} } }$ , $5.15+1.96 \times {\frac{1.68}{\sqrt{4400} } }$ ]

= [5.10 , 5.20]

Therefore, 95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

8 0

3 years ago

Trey is renting a paddleboard he paid $6 per hour plus a $10 rental fee he had $30 to spend how many hours can you rent a paddle

Trava [24]

3 hours

6x+10 is less than or equal to 30

8 0

3 years ago

Read 2 more answers

For every 15 minutes of a show, there are two minutes to commercial. At this rate, if leila has seen 45 minutes of a show, how m

Ainat [17]

Answer:

51 minutes.

Step-by-step explanation:

We have been given that for every 15 minutes of a show, there are two minutes to commercial. At this rate, Leila has seen 45 minutes of a show. We are asked to find the time for which Leila has been watching TV.

We will use proportions to solve our given problem.

$\frac{\text{Minutes of TV show + Advertisement}}{\text{Minutes of TV show}}=\frac{15+2}{15}$

$\frac{\text{Minutes of TV show + Advertisement}}{\text{Minutes of TV show}}=\frac{17}{15}$

Upon substituting our given values, we will get:

$\frac{\text{Minutes of TV show + Advertisement}}{45}=\frac{17}{15}$

$\frac{\text{Minutes of TV show + Advertisement}}{45}\times 45=\frac{17}{15}\times 45$

$\text{Minutes of TV show + Advertisement}=\frac{17}{1}\times 3$

$\text{Minutes of TV show + Advertisement}=51$

Therefore, Leila has been watching TV together for 51 minutes.

8 0

3 years ago

-7x^3-9x^2+8x this is factoring completely

loris [4]

Answer:
 (x + 6) • (x + 5) • (x - 2)

Is this what u were looking for? Sorry if not XDD

3 0

3 years ago

Read 2 more answers

The surface area of a cube is 864 in.2. Find the volume of the cube

Sveta_85 [38]

As the cube has 6 faces the area of one face will be 864 / 6 = 144 in^2

so each edge = 12 in

Volume of cube = 12^3 = 1728 in^3

3 0

3 years ago