Download Warm up activity I have a 35% chance of winning a game. Let X be

Warm up activity
I have a 35% chance of winning a game. Let X be the # of wins if I play 4 times.
Create the Probability Distribution
X
P(X)
0
1
2
3
4
Prob. Distribution Directions:
 Put the x-values in L1
 Go to the TOP of L2
 Type in binompdf(4, 0.35, L1)
 Be sure that you don’t type in L1, but you put in the
name of L1 from your list names.
 Hit ENTER
 This will give you each probability for the table at left
Create a histogram:
Histogram Directions:
 Go to STAT PLOT
 Go into Plot 1, and make it a histogram
 Under X-list, put L1
 Under Freq, put L2
 Hit Zoom 9
 You will probably need to adjust your
Window. Make your min 0 and max 5,
and make your bar width 1.
Describe the shape of the histogram:
Now let’s change the sample size to 10. Create the distribution, then the histogram. (Use the same directions as
above, but with n=10)
Distribution:
X
Histogram:
P(X)
0
1
2
3
4
5
6
7
8
9
10
Describe the shape of the histogram:
Now let’s change the sample size to 20. Create the distribution, then the histogram.
Distribution:
X
P(X)
X
0
11
1
12
2
13
3
14
4
15
5
16
6
17
7
18
8
19
9
20
P(X)
10
Histogram:
Shape:
Try it with a sample size of 50. Just create the distribution and histogram in your calculator. What is the shape
of this histogram??
What do you notice about the shape of the distribution as the sample size increases? We have a specific NAME
for these types of distributions…. (unimodal, bell shaped, symmetric… starts with an “N”)
Ch. 17: Probability Models: Binomial Random Variables: LARGE SAMPLE SIZE
What happens to the shape of the Binomial Random Variable when n is large?
It looks more and more NORMAL!
What is considered a “large enough” n (for the shape to look normal)??
We do a “check” to see if n is large enough for it to look normal:
np  10
n(1  p )  10
So if the check passes…
 We can say that the distribution is approximately normal, and can use normal functions!

Calculator: normalcdf(lower bound, upper bound, mean, std. dev)

Same mean and std dev. that we learned yesterday:
 X  np
 X  np(1  p)
Example 1:
It is said that 75% of people pay their credit card bill on time. If we take a sample of 125 adults, what is the
chance that over 80 of them paid their bill on time this past month?
n = 125
p=0.75
Since the check passes, the distribution looks normal and we can use normalcdf!
Check :
np  93.75
 10
P(X>80) = normalcdf(80, E99, (125*0.75),
125*0.75*0.25 ) = 0.9977
n(1  p )  31.25
Example 2:
Assume 15% of adults jog regularly. We survey 1,000 adults what is the probability that between 120 and 160
people in our sample jogs?
n = 1000
Check :
np  150
p=0.15
 10
Since the check passes, the distribution looks normal and we can use normalcdf!
P(120<X<160) = normalcdf(120, 160, (1000*0.15),
n(1  p )  850
= 0.8081
1000*0.15*0.85 )
AP STAT- Ch. 17: Binomial Normal Approximations
1. Determine whether each binomial distribution (with given n and p) can be approximated with the normal
distribution. (does the check pass??)
a. n = 30, p = .5
b. n = 50, p = .9
c. n = 40, p = .8
2. For each of the following values of p, determine the minimum sample size need to use the normal
approximation. (the minimum n so that the check passes)
a. p = .1
b. p = .3
c. p = .8
For the following, don’t forget to do the check first!!!
3. An airline company has found that 5% of its passengers do not show up for their scheduled flights. If a plane
has 700 seats, find the probability that 50 or more people will not show up for the fully booked flight.
4. It is estimated that 48% of all motorists use their seat belts. If a police officer observes 400 cars go by in an
hour, what is the probability that the proportion of drivers wearing seat belts is between 45% and 55%?
5. Suppose that 70% of all dialysis patients will survive for at least 5 years. If 100 new dialysis patients are
selected at random, what is the probability that the proportion surviving for at least 5 years will exceed 80%?
6. Of all five-year-old children, 56% are enrolled in school. If a sample of 1500 such children is randomly
selected, find the probability that at least 750 will be enrolled in school.
7. A surgical procedure is successful 80% of the time. In a random sample of 100 patients, find the probability
that the sample proportion is within .01 of the mean.
8. Say that 37% of households have a VCR. What is the probability that in a random sample of 250 households,
the sample proportion differs from the mean by more than .03?
9. A car dealer states that 90% of all automobiles sold have air conditioning. If the dealer sells 1000 cars, find
the probability that fewer than 100 of them will not have AC.
10. Find the probability that in 2000 births, between 975 and 1050 will be female.