Based on historical data, your manager believes that 39% of the company's orders come from first-time customers. A random sample of 171 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.21 and 0.32

And we can find the probability with this difference:

Step-by-step explanation:

For this case we have the following info given:

represent the sample size

the proportion of interest

We want to find the following probability:

We can use the normal approximation for this case since np >10 and n (1-p) >10

For this case we know that the distribution for the sample proportion is given by:

And we can use the following parameters:

And we can apply the z score formula given by:

And using this formula we got:

And we can find the probability with this difference:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.