Hi,

  5.355<  < 5.445    ||Note:(.445-.355)/2 = .045= ME

  5.4 -.045<  < 5.4 + .045 

re: n = 200, m = 55200 and SD = 1500 

Find a 95% confidence interval for the true mean annual income of the nursing school alumni.

  ME = 1.96(1500/sqrt(200))}}} = $207.89

55200 - ME <  < 55200 + ME

 

Hi,

Note:  Bell shaped Curve showing placement of z = 0, z = ±1, 2, 3 

Left or Right of z = 0 being 50% of the area under the standard normal curve...

The area under a normal curve = 1



As to: A set of data is normally distributed with a mean of 85 and SD of 4.59 

x = 90 

 z = (90-85)/4.59 = 1.089  

Exel function NORMSDIST(1.089) = .862 , 86.2% to the left and 13.8% to the right



As:a normal distribution with mu = 25 and sigma = 9, if z = -2, 

then z = (x -25)/9 = -2,   and   x =  -18 + 25 = 7

 

Hi,

Which of the following lines is equidistant fro the points 

(3,8) and 

(9,6)   m = 2/-6 = -1/3   and y = (-1/3)x + 9

any line parallel to above line would be equidistant from these points.  

D.  y = (-1/3)x would be, same slopes m = (-1/3)

 

Hi,

7x + 12 > 6x - 15

solving for x:

 x > -27

x can be any real number to the right of x = -27 on the number Line

 

Hi,

Construct the indicated 98% confidence interval for the population mean u using a t-distribution.

c=0.98, x=114, s=10, n=27, Degrees of Freedom = (n-1)= 26, See Below:

 ME = 2.78(10/sqrt(27))

X = 114  

  114 - ME <  < 114 + ME

DOF 	Probability, p			

	0.1	0.05	0.01	0.001

1	6.31	12.71	63.66	636.62

2	2.92	4.3	9.93	31.6

3	2.35	3.18	5.84	12.92

4	2.13	2.78	4.6	8.61

5	2.02	2.57	4.03	6.87

6	1.94	2.45	3.71	5.96

7	1.89	2.37	3.5	5.41

8	1.86	2.31	3.36	5.04

9	1.83	2.26	3.25	4.78

10	1.81	2.23	3.17	4.59

11	1.8	2.2	3.11	4.44

12	1.78	2.18	3.06	4.32

13	1.77	2.16	3.01	4.22

14	1.76	2.14	2.98	4.14

15	1.75	2.13	2.95	4.07

16	1.75	2.12	2.92	4.02

17	1.74	2.11	2.9	3.97

18	1.73	2.1	2.88	3.92

19	1.73	2.09	2.86	3.88

20	1.72	2.09	2.85	3.85

21	1.72	2.08	2.83	3.82

22	1.72	2.07	2.82	3.79

23	1.71	2.07	2.82	3.77

24	1.71	2.06	2.8	3.75

25	1.71	2.06	2.79	3.73

26	1.71	2.06		3.71

27	1.7	2.05	2.77	3.69

28	1.7	2.05	2.76	3.67

29	1.7	2.05	2.76	3.66

30	1.7	2.04	2.75	3.65

 

Hi,

Find the critical value tc for the confidence level c=0.99 and sample size n=26

Note: Degrees of Freedom = (n-1) = 25, You may find Below table useful in Your studies

DOF	Probability, p			

	0.1	0.05	0.01	0.001

1	6.31	12.71	63.66	636.62

2	2.92	4.3	9.93	31.6

3	2.35	3.18	5.84	12.92

4	2.13	2.78	4.6	8.61

5	2.02	2.57	4.03	6.87

6	1.94	2.45	3.71	5.96

7	1.89	2.37	3.5	5.41

8	1.86	2.31	3.36	5.04

9	1.83	2.26	3.25	4.78

10	1.81	2.23	3.17	4.59

11	1.8	2.2	3.11	4.44

12	1.78	2.18	3.06	4.32

13	1.77	2.16	3.01	4.22

14	1.76	2.14	2.98	4.14

15	1.75	2.13	2.95	4.07

16	1.75	2.12	2.92	4.02

17	1.74	2.11	2.9	3.97

18	1.73	2.1	2.88	3.92

19	1.73	2.09	2.86	3.88

20	1.72	2.09	2.85	3.85

21	1.72	2.08	2.83	3.82

22	1.72	2.07	2.82	3.79

23	1.71	2.07	2.82	3.77

24	1.71	2.06	2.8	3.75

	1.71         2.06        2.79	 3.73

26	1.71	2.06	2.78	3.71

27	1.7	2.05	2.77	3.69

28	1.7	2.05	2.76	3.67

29	1.7	2.05	2.76	3.66

30	1.7	2.04	2.75	3.65

 

Hi,

Note:  Bell shaped Curve showing placement of z = 0, z = ±1, 2, 3 

Left or Right of z = 0 being 50% of the area under the standard normal curve...



As to A set of data is normally distributed with a mean of 70 and SD of 4. X = 68 

 z = (68-70)/4 =

Exel function NORMSDIST(-.5) = .3085 , 30.85% to the left and 69.15% to the right

 

Hi,

Note:  Bell shaped Curve showing placement of z = 0, z = ±1, 2, 3 

Left or Right of z = 0 being 50% of the area under the standard normal curve...



As to A set of data is normally distributed with a mean of 100 and SD of 15. X = 90 

 z = (90-100)/15 =

Exel function NORMSDIST(-.6667) = .25 , 25% to the left and 75% to the right

What percentage of scores is between 100 and 90? 25%

· What would be the percentile rank for a score of 90? 25%

 

Hi,

Note:  Bell shaped Curve showing placement of z = 0, z = ±1, 2, 3 

Left or Right of z = 0 being 50% of the area under the standard normal curve...



As to z = .09, is placed slightly right of center on the standard normal curve..

Exel function NORMSDIST(.09) = .5359 , 54% to the left and 46% to the right

 

Hi,

-2x+7y=-7   or y = (2/7)x - 1

Plot (0,-1) & (3.5,0) and connect with Line

 

Hi,

In a survey of 9000 women, 6431 sy they change their nail polish once a week.

 Construct a 90% confidence interval for the population proportion of women who change their nail polish once a week.

 p = 6431/9000 = .715   and q = .285

ME = 1.645

X  = 6431

  6431 - ME <  < 6431 + ME

 

Hi,

4/3 + 2/3x = 31/12 + 5/4x + 3/4

use a  common Denominator of 12 and then solve for x

 

    

    

      x = 

 

 

Hi,

x -2y = -8   or  y = (1/2)x + 4

Finding the y-intercept when x = 0  (, _)  

 -2y = -8 

      y = 4    || the y-intercept  (, 4) 



Finding the x-intercept when y  = 0  ( _, )   

 x -2· = -8 

     x = -8     ||   the x-intercept is (-8 , ) 

Plot (0,4) and (-8,0) and connect with a Line

 

Hi,

If p = 2(L+B)...

 p/2 = L + B

 

 

Hi,

Find the minimum sample size n needed to estimate u for the given values of c, s, and E.



c=0.98, s=8.4, and E=2





    n = 95, the minimum sample size needed 

 

Hi,

Find the margin of error for the given values of c, s, and n.

c=0.95, s=3.1, n=49

 ME = 

 

Hi,

Construct the 90% confidence interval for the population mean u.

X  = 15.5

 s =7.0, and n=85

 ME = 

  15.5 - ME <  < 15.5 + ME

 

Hi,

A student randomly guesses on a 10 question true/false exam. Minimum threshold for a B grade is 80%.  

Find the probablility the student gets at least a B on the exam.

Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p & q are = 1/2 or .5

nCx = 

P(x≥ 8) = P(8) + P(9) + P(10)  

P(8) = 10C8(.5)^8(.5)^2  = 45(.5)^8(.5)^2 = .044

P(9) = 10C9(.5)^9(.5)^1 =10(.5)^9(.5)^1 = .01

P(10) = 10C10(.5)^10(.5)^0 =1*(.5)^10(.5)^0 = .001

P(x≥ 8) = P(8) + P(9) + P(10) = .055

 

Hi,

 

Hi,

Note: A is area, s is length of the side and P is the Perimeter of each garden

A square garden plot measures 180 square feet. 

, P = 

A second square garden plot measures 405 square feet. 

, P =



 

 

Hi,

Machine A can print 20 posters in a minute and machine B can print 15 posters a minute.

Note: together A and B can do 35 Posters/min

How long will it take both of machines to print 945 if they work together? 

 

 

Hi,

if five men can do a piece of job in twenty-five days, 

how many days will it take ten men to do the same job working at the same rate?

  

  

 

Hi,

Train A leaves the platform at 5 pm at a speed of 120 km/h and train B leaves the same platform 

on a parallel track in the same direction at 7 30 pm at 144 km/h. 

After how many hours will train B cross train A?

 D = rt

 Distance = Distance

 

solving for x

  x = 

 

Hi,





 Parbola opening to the Right V(5,-3) y = -3 line of symmetry

 

Hi,

f(x) = -7x^3-4x^2-8x+1

f(-4) = (-7)(-64) - 4(16) -8(-4) + 1 = 417

 

Hi,

y=x^2+2x+4   Note:  (0,4)is where Parabola crosses the y axis

y = (x+1)^2 -1 + 4

   V(-1,3) Yes!  Important 1st Step

For graphing:

2nd step: Which direction does the Parabola Open? 

 y = a(x-h)^2 + k   is the general form of a parabola opening Up or Down, a = 1 > 0, parabola opens Up

3rd Step:  what is the Line of symmetry:  x = -1

Plotting Vertex and y-intercept and putting in the line of symmetry,

 allows us to determine the graph

 

Hi,



   -7 < x < 7

 

Hi,

    ||Cross Multiplying to solve

   5n = 6(n-2)

   5n = 6n - 12)

   12 = n

 

Hi,

convert 2x+y=12 to y-intercept form: y = mx + b

2x+y=12    ||solving for y

 y = -2x + 12

 

Hi,

Re TY, As to demominator : 

Puting in terms of  (Using a common denominator)allows us to work together with the numerator more easily

 

Hi,

-9(6m-3)+6(1+4m)     ||Distributing the -9  and 6

 -54m + 27 + 6 + 24m  ||Combining Like terms

 -30m + 33