A random sample of adult men was asked if they would return the money if they found a wallet on the street. Of 143 men, 29 said they would. The true proportion of all adult men who would return the money is 18%. Which of the following do you expect would accurately describe the sampling distribution of the sample proportion of men would return money from a found wallet? Select one or more:
a. The mean of the sampling distribution will be equal to 0.18.
b. The mean of the sampling distribution will be equal to 0.2028.
c. The sampling distribution would be approximately standard normal.
d. The sampling distribution will be skewed right.
e. The sampling distribution will be skewed left.
f. The sampling distribution will be approximately normal.
g. The standard deviation of the sampling distribution will be 0.0336.

b. The mean of the sampling distribution will be equal to 0.2028.

f. The sampling distribution will be approximately normal.

g. The standard deviation of the sampling distribution will be 0.0336.

Step-by-step explanation:

We use the Central Limit Theorem to solve this question.

Central Limit Theorem:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation .

The sample proportion being approximately normal means that option f. is correct.

Of 143 men, 29 said they would.

This means that

This means that option b is correct.

g. The standard deviation of the sampling distribution will be 0.0336.

Lets find the standard deviation.

Sample of 143, so

So option g. is correct.

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

the 4th choice is the correct one

step-by-step explanation: