MATH 302 University of Arizona Global Campus Statistics Questions
Normal Distributions are the most common distributions in statistics. If a randomvariable X is normally distributed with a mean μ and a standard deviation σ.
X ~ N(μ, σ) ; Z ~ N(0, 1)
Normal distributions are known as “bell-shaped curve”
To find the probabilities of normal distributions using a Normal Distribution Table,
we would start by converting the x values to a standard normal z-curve. The
equation of the z – score;
?−?
?=
?
Nowadays, we do not need to do this conversion to the standard normal
distribution, since Excel does it automatically for us.
Excel can only find Less Than probabilities, therefore it is important to make sure
that your problem is only including the less than inequality ( 25,000) = 1 – NORM.DIST(25000,25650,1560.09,TRUE)
In Excel make sure you hit the “=“ sign first, then the 1 – and then start typing in
NORM.DIST(. From here make sure you include the left parenthesis then type in the
x value, the mean, the standard deviation, then either True. Then close the
parenthesis ) and hit Enter.
The probability that the sample mean for the new sample of 5 cars is below
$25,000 is 66.15%.
Remember: Once you hit “Enter” the answer returns a decimal. You need to
convert it to a percentage if you want to read a percentage.
3. Assume that 5 additional cars are randomly sampled, and their prices are
recorded. What is the probability that the sample mean price of the 5 new cars will
be between $24,000 and $25,000?
Because of the word “between”, we want to find this probability
P(24000 < ?̅< 25000). Since we are using the same data the mean and the new SD
will be the same. Remember the function in Excel are in the less than form. This
means we will need to do an extra step in Excel to get the probability we want.
P(24000 < ?̅ < 25000) = P(?̅ < 25000) – P(?̅ < 24000)
= NORM.DIST(25000, 25650, 1560.09,TRUE) - NORM.DIST(24000,25650,1560.09,TRUE)
In Excel make sure you hit the “=“ sign first, then start typing in NORM.DIST(. From
here make sure you include the left parenthesis then type in the x value, the mean,
the standard deviation, then either True. Then close the parenthesis ), hit the minus
– sign then Repeat and then hit Enter.
The probability that the sample mean for the new sample of 5 cars is between
$24,000 and $25,000 is 19.34%.
Remember: Once you hit “Enter” the answer returns a decimal. You need to
convert it to a percentage if you want to read a percentage.
Vehicle type/Class
Year
CAR
2017
CAR
2018
CAR
2019
CAR
2020
CAR
2015
CAR
2020
CAR
2019
CAR
2019
CAR
2020
CAR
2018
Qualitative Qualitative
Make
BMW
Volkswagen
Honda
Subaru
Mitsubishi
Ford
Chevrolet
Nissan
Dodge
Audi
Qualitative
Model
M2
Golf R
Civic Type R
WRX STI
Lancer Evo
Mustang GT
Camaro 2SS
370Z Nismo
Charger Scat
TT
Qualitative
Mean:
Median:
SD:
Sample size:
Price
$40.999
$40.000
$41.498
$40.435
$45.198
$44.095
$43.895
$42.990
$45.000
$46.247
Quantitative
$43.036
$43.443
2190,91174
10
MPG (city)
21
21
22
16
17
15
16
17
15
23
Quantitative
MPG(highway)
26
29
28
22
23
24
24
26
24
30
Quantitative
Horsepower
365 hp
292 hp
306 hp
310 hp
303 hp
460 hp
455 hp
350 hp
485 hp
220 hp
Quantitative
Price
Mean
43035,7
Standard Error692,827124
Median
43442,5
Mode
#N/A
Standard Deviation
2190,91174
Sample Variance
4800094,23
Kurtosis
-1,512995
Skewness
-0,0663174
Range
6247
Minimum
40000
Maximum
46247
Sum
430357
Count
10
Confidence Level(95.0%)
1567,28384
