A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of 114 students

in the high school and found a mean of 195 messages sent per day with a standard

deviation of 73 messages. Determine a 95% confidence interval for the mean,

rounding all values to the nearest whole number.

 182   ≤  x  ≤  208    Confidence Interval

Step-by-step explanation:

Normal Distribution

Sample size     n = 114

Sample mean     X  =  195

Sample standard deviation   σ = 73

Confidence Interval  (CI)  95 %     means   α = 5 %         α/2  = 0,025

Values from Z table for  α/2  = 0,025

Z  = -1,97           Z = 1,97

Confidence Interval:

CI           X  - Zα/2* σ/√n   ≤  x  ≤    X  - Zα/2* σ/√n

σ = 73      and  n = 114

73/√114  =  73/10,677   = 6,84

CI     195   - (1,97)* 6,84    ≤  x  ≤    195 + (1,97)* 6,84

        195  -  13,47   ≤  x  ≤   195  + 13,47

        181,53    ≤  x  ≤    208,47

According to rounding criteria

        182   ≤  x  ≤  208

step-by-step explanation:

bob the banana

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!