Mean 4 Median 4 Std dev 224 CH 2 If the mean is greater than the median the distribution is skewed right If the mean is less than the median the distribution is skewed ID: 808742
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Slide1
STA 2023
Slide2
Slide3CH. 2
Find the mean, median, and standard deviation of the data set { 5, 4, 7, 3, 1 }
Mean =
4
Median=
4
Std. dev.= 2.24
Slide4CH. 2
If the mean is
greater
than the median, the distribution is skewed
right
.
If the mean is
less
than the median, the distribution is skewed
left
.
If the mean is
equal
to the median, the distribution is
not skewed
.
Slide5CH. 2
A football team scores an average of 20 points a game with a standard deviation of 3 points.
T
he distribution is approximately normal. (a) What is the probability that the team scores between 17 and 23 points? (b) Between 14 and 23 points?
a.)
About
68%
b.)
About
81.5%
Slide6CH.2
The mean of a data set is 8 with a std. dev. of 1.5. If we don’t know the shape of the distribution, what is the probability between 6.5 and 9.5? Between 5 and 11?
Chebychev
: 1- 1/k
2
Where k is the number of St.
Devs
away from the mean.
Answer=
At least
0%
Answer=
At least
75%
Slide7CH. 3
What is the difference between multiplicative, combination, and permutation?
Multiplicative: Just looking to find how many possible outcomes per trial “x” from “n” number of trials. (X)
n
Combination: Number of ways we can select n items from N items without replacement.
Use when
order doesn’t matter
.
Slide8CH. 3
Permutation: Number of ways we can put n things out N in order.
Use when order matters!
Slide9CH. 3
How many ways can we choose 5 flavors of ice cream out of 21? How many ways can we put 3 flavors in order from first to third?
Answer:
Answer:
Slide10CH. 3
Currently Whipping
Currently Nene
Total
Done Whipping
3
15
18
Done
with
Nene
7
8
15
Total
10
23
33
Find Probability of these dance combinations according to the table: (a) Done whipping or currently Nene; (b) Finished Nene and currently Nene
Slide11CH. 3
Answer (a):
Answer (b):
Slide12CH. 3
If P(A)= 0.3, P(B)= 0.5, and P(A U B)= 0.65:
(a) what is P(A
∩
B)?
(b) Are A and B independent?
Slide13CH. 3
a.)
b.)
If independent,
Since
, A and B are
independent
Slide14CH. 4
(a) Find μ and σ
(b) Find P(x=5); P(x≤ 7); P(x > 2)
a.) μ= 4.1; σ= 1.67
b.) P(x=5)= 0.35; P(x≤ 7)= 1; P(x > 2)= 0.8
X
2
3
5
7
P(x)
0.20
0.30
0.35
0.15
Slide15CH. 4
You play roulette and place a $10 bet on red.
There are 18 red spaces, 18 black spaces, and 2 green spaces.
What is the expected result of your bet?
Probability of red (success)= 18/38
Probability of black (failure) = 18/38
Probability of green (failure) = 2/38
Success= 18/38 Failure= 20/38
Slide16CH. 4
(gain) x P(success) – (lose) x P(failure)
(10) X (18/38) – (10) x (20/38)
4.74 – 5.26 =
-$0.52
We should expect to lose money.
Slide17CH. 4
How do you know when to use binomial or Poisson?
Binomial: 2 possible outcomes (success and fail).
Poisson: Use when dealing with time/rate.
where
and x=number of successes we are interested in.
Slide18CH. 5
The average semester grade in STA 2023 is 70 with a standard deviation of 3.5. What is the probability that the average grade this semester will be greater than 76? Less than 72? Equal to 68?
Answer: 0.50 – 0.4564 = 0.0436
Answer
:
0.50 + 0.2157 = 0.7157
Answer: Cannot be equal to a number because these are continuous random variables. P = 0.
Slide19CH. 5
The average grade in STA 2023 is 70 with a standard deviation of
6
. If you want to be in the 98
th
percentile, what is the minimum score you must obtain?
Answer: 85.3
Slide20CH. 6
We want to find out how many times Detroit Lions fans cry themselves to sleep per week. We randomly sample 40 Lions fans from a population with a mean of 5 and std. dev. of 1.5. What is the probability that the mean of our sample will be more than 4.5?
L
ess than 4?
P= 0.50 + 0.4826 = 0.9826
P= Our Z-score is -4.22. This is too negative to look up, so we assume P<-4.22 = 0
Slide21CH. 7
At a set level of confidence, does our confidence interval increase or decrease as sample size increases?
Answer: Decreases
Slide22CH. 7
At a set sample size, what happens to our confidence interval as our level of confidence increases?
Answer: Increases
Slide23CH. 7
If constructing interval for
When n
When n
If finding n:
Slide24CH. 7
If constructing interval for P:
When n
When n
If finding n:
Note: When finding n, if
is unknown use 0.50.
Slide25CH. 7
Construct a C.I. at 95% confidence with a sample mean of 70 and a std. dev. of 20 when n=49. When n=25
Answer = 70
5.6 = (64.4, 75.6)
Answer = 70
Slide26CH. 7
30 pre-med students out of a sample of 40 say they have stress-induced acid reflux. Construct a 90% confidence interval to estimate the true proportion of pre-med students with stress-induced acid reflux.
Answer = 0.75
0.11 = (0.64, 0.86)
Slide27CH. 7
Determine the sample size needed to construct a 99% C.I. to estimate the true proportion to within 0.10 with
= 0.60. What if we didn’t know
Slide28CH. 8
It is believed that the average grade on STA 2023 final exams is 70. A study of 36 students was run, and the results yielded a mean of 76 with a standard deviation of 18. Is this enough evidence to claim that the true mean score is greater than 70 at
What is the level of significance?
Answer: Yes, our test statistic lies in the RR;
P=0.0228.
Slide29CH. 8
It is estimated that 70 percent of college students enjoy going to Chipotle. A sample was conducted where 23 out of 29 students sampled said that they enjoy Chipotle. Is this
e
nough evidence to say that more than 70 percent like Chipotle at
.
Answer: No, our T.S. of 1.09 does not fall in the RR t>1.28.
Slide30CH. 9
A study was run to see if there is a difference in mean test scores between students who play piano, and students who do not. 20 piano students and 18 non-piano students were studied. The mean of the piano group was 85 with
s.d.
of 8, and the mean of the non-piano group was 81 with
s.d.
equal to 7.5. Is this enough evidence to conclude that there is a difference at
Construct a 95% C.I.
Slide31CH. 9
T.S.
Answer: Test stat is not in RR, do not reject.
Answer:
Slide32Hopefully you now feel less like this
Slide33And more like Sheldon
https://www.youtube.com/watch?v=ay3dSzkfswE