(a) Data with the eight day's measurement.
Raw data: [60,58,64,64,68,50,57,82],
Sorted data: [50,57,58,60,64,64,68,82]
Sample size = 8 (even)
mean = 62.875
median = (60+64)/2 = 62
1st quartile = (57+58)/2 = 57.5
3rd quartile = (64+68)/2 = 66
IQR = 66 - 57.5 = 8.5
(b) Data without the eight day's measurement.
Raw data: [60,58,64,64,68,50,57]
Sorted data: [50,57,58,60,64,64,68]
Sample size = 7 (odd)
mean = 60.143
median = 60
1st quartile = 57
3rd quartile = 64
IQR = 64 -57 = 7
Answers:
1. The average is the same with or without the 8th day's data. FALSE
2. The median is the same with or without the 8th day's data. FALSE
3. The IQR decreases when the 8th day is included. FALSE
4. The IQR increases when the 8th day is included. TRUE
5. The median is higher when the 8th day is included. TRUE
Answer:

Step-by-step explanation:
Given

Required
The standard form of the polynomial
The general form of a polynomial is

Where k is a constant and the terms are arranged from biggest to smallest exponents
We start by rearranging the given polynomial

Given that the highest exponent of x is 5;
Let n = 5
Then we fix in the missing terms in terms of n

Substitute 5 for n


Hence, the standard form of the given polynomial is 
Answer:
a)
And we can find this probability with this difference:
And using the norma standard distribution or excel we got:
b) 
And using the complement rule we got:

Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where
and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference:
And using the norma standard distribution or excel we got:
Part b
For this case we want this probability:

And we can use the z score and we got:

And using the complement rule we got:

Answer:
Igloo Ice has the lowest delivery charge.
Step-by-step explanation:
Igloo Ice when you plug in 120 for the y you get 25.714 as the x.
Freds freeze at 120 is 20.
And lastly Tasty treats at 120 is 24, so Igloo Ice has the lowest delivery charge per person (you pay $120 for 25.714 people.)