Olson Quiz #5
5/14/2012
(1)
If you flip an unfair coin 14 times (the coin gets heads 65% of the time),
what is the probability of getting exactly 9 heads?
For this you must use the equation for probability:
P(y) = C(n,y)*py*q(n-y) ,
where n= 14, p=0.65 (so q=1-0.65=0.35) and y=9
P(9) = C(14,9)*(0.65)9*(0.35)5 = 0.2178
(2)
What is the mean and standard deviation of a binomial experiment in
which n=20 and p=0.7?
mean = n*p = 20*0.7 = 14
std dev = Sqrt(n8p8q) = sqrt(20*0.7*0.3) = 2.0493
(3)
Binomial experiment: n=20 and p=0.6 Find the following probabilities
using the table:
a. P[X<7] = 0.021
b. P[X>10] = P[X>11] = 1 - P[X<10] = 1 - 0.245 = 0.755
c. P[6<X<13] = P[X<13] - P[X<6] = 0.750 - 0.006 = 0.744
(4)
Given the following continuous probability distribution…
0.4
0.2
0.2
0.1
0.1
2
3
4
5
6
7
a. What is the probability of getting greater than 5?
Add the areas from 5 to 7
(6-5)*0.2 = (7-6)*0.1 = 0.2 + 0.1 = 0.3
b. What is the probability of getting between 3.5 and 5?
Add the areas from 3.5 to 5
(4-3.5)*0.2 = (5-4)*0.4 = 0.1 + 0.4 = 0.5
(5)
A normal distribution with a mean of 60 and a variance of 9.
For these problems you must know the z-score equation:
z-score = (x-μ)/σ and that though given the variance you NEED the
standard deviation (which is the square root of the variance) = 3
a. P[X>65] = P[(X-μ)/σ >(65-60)/3] = P[z>1.67]
Draw the picture and the probability from the table, and you will
see that the answer is 0.5 - 0.4525 = 0.0475
b. P[55<X<67] = P[ (55-60)/3 < (X-μ)/σ <(67-60)/3] = P[-1.67<z<2.33]
Draw the picture and the probability from the table, and you will
see that the answer is 0.4525 + 0.4901 = 0.9426
c. P[55<X<59] = P[ (55-60)/3 < (X-μ)/σ <(59-60)/3] = P[-1.67<z<-0.33]
Draw the picture and the probability from the table, and you will
see that the answer is 0.4525 – 0.1293 = 0.3232
d. What is the cut-off for the top 33%?
This becomes 0.33 = P[X>x] = P[ (X-μ)/σ <(x-60)/3] = P[z> (x-60)/3]
Draw a picture. You will note that the probability from the mean
to x is 0.1700. Now using the table (backwards) finding a z-score for
a probability of 0.1700…you get a z = 0.44, so 0.44 = (x-60)/3,
therefore x = 61.32