Data from the bureau of labor statistics’ consumer expenditure survey show that annual expenditures for cellular phone services per consumer unit increased from $237 in 2001 to $634 in 2007. let the standard deviation of annual cellular expenditure be $52 in 2001 and $207 in 2007. a. what is the probability that the average annual expenditure of 125 cellular customers in 2001 exceeded $220? (round answer to 4 decimal places.) b. what is the probability that the average annual expenditure of 125 cellular customers in 2007 exceeded $607? (round answer to 4 decimal places.)

a) 0.9998      

b) 0.9264        

Step-by-step explanation:

Given:

Annual expenditures for cellular phone in 2001 = $237

Annual expenditures for cellular phone in 2007 = $634

standard deviation of annual cellular expenditure in 2001 = $52

standard deviation of annual cellular expenditure in 2007 = $207

a) P( average annual expenditure of 125 cellular customers in 2001 exceeded $220)

= P(X > $220)

Now,

Z value =

Here,

σ = standard deviation

n = sample size

Thus,

P(X > $220) =

or

=

or

= P( Z > -3.65 )

= 0.9998      [From z table ]

b) P( average annual expenditure of 125 cellular customers in 2007 exceeded $607)

= P(X > $220)

Now,

Z value =

Here,

σ = standard deviation

n = sample size

Thus,

P(X > $220) =

or

=

or

= P( Z > -1.458 )            

= 0.9264         [From z table ]

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

111

step-by-step explanation: