Answer:

And we can find the individual probabilities using the probability mass function and we got:


And replacing we got:

Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
For this case we want this probability:

And we can use the complement rule and we got:

And we can find the individual probabilities using the probability mass function and we got:


And replacing we got:

Answer:
The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which
z is the z-score that has a p-value of
.
A store randomly samples 603 shoppers over the course of a year and finds that 142 of them made their visit because of a coupon they'd received in the mail.
This means that 
95% confidence level
So
, z is the value of Z that has a p-value of
, so
.
The lower limit of this interval is:

The upper limit of this interval is:

The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).
We will check each options and verify it
(a)

we can plug m=2



so, this is FALSE
(b)

we can plug x=3



so, this is TRUE
(c)

we can plug x=3



so, this is FALSE
(d)

now, we can plug x=2



So, this is FALSE
Answer:
23/21
Step-by-step explanation:
The slope is computed from ...
m = (y2 -y1)/(x2 -x1)
For the given points, the slope is ...
m = (26 -3)/(18-(-3)) = 23/21
The slope of the trend line is 23/21.
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