Self-assessment exam C
Probability Distributions - answers
Binomial-Poisson-Normal-Sampling distribution of the mean
Name: ____________________________
1-2. Complete:
a) In a binomial distribution with n=400 and p=0.3, the mean =___120_____
b) In a binomial distribution with n=400 and p=0.3, the standard deviation =_9.16515139______
c) The mean of the standard normal distribution is ___0____.
d) The standard deviation of the standard normal distribution is __1______.
e) The only parameter of the Poisson distribution is ______p___
f) The parameter of the geometric distribution is __mean______
g) In the standard normal distribution the z-value below which we have a 40% probability is _-0.253347___
invNorm(0.40)= -0.253347
h) In a standard normal distribution, the P(x>-1.43) = ___0.9236414449__________
normalcdf(-1.43, 10^9)= 0.9236414449
i) In a binomial problem with n=70, p=0.18, P(x> 12) = __0.4990102337_____
1 - binomialcdf(70, 0.18, 12) = 0.4990102337
j) In a normal distribution with mean   40 and   3.5 , the ordinate at x=40 is 0.1139835087__
normalpdf(40, 40, 3.5) =0.1139835087
3. Five percent (5 %) of all TVs manufactured by a certain electronics company are defective. A quality control
inspector randomly selects a sample of 40 TVs from the production line. What is the probability
a) more than 2 of them are defective?
Binomial: n=40, p=0.05, x>2
Answer: 1 - binomialcdf(40, 0.05, 2)= 0.3232642405
b) none of them are defective?
Answer: binomialpdf(40, 0.05, 0) =0.1285121566
a
0.3232642405___
b) 0.1285121566
4. A washing machine In a Laundromat breaks down at an average of three times per month. Find the
probability that during the next month this machine will have
Poisson   3 breaks down per month
a) at most 1 breakdowns
Poissoncdf ( 3, 1)=0.1991482735
a) 0.1991482735
b) exactly 21 breakdowns
Poissonpdp (3, 21)  1.01933982  10
b)
-11
0.0000000000101933982
 0.0000000000101933982
5. The probability that a baseball player hits a home run during a game is 0.15. Assuming that this probability
remains the same for the whole baseball season, what is the probability that the player will hit his first home run
after the 3rd game?
Geometric: p=0.15, x>3
Answer: 1 - geometriccdf(0.15, 3) = 0.614125
answer: = 0.614125
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6. In selecting at random sample of 5 students from a class of 30 students, what is the probability that the
sample will be composed of 3 female students and 2 male students?. In the class there are 18 females students
and 12 males students. Use the Hyper-geometric distribution.
C  C
816  66
P(x  3 females )  18 3 12 2 
 0.3779209296
142506
30 C5
6.
0.3779209296 ___
7. A normally distributed random variable x possesses a mean of 65 and a standard
deviation of 3.4. Find the probability that
a) a value of x falls between 62 and 66.
a) _0.4268729858___
Answer: Normalcdf(62, 66, 65, 3.4) = 0.4268729858
b) Find the 60th. percentile of the distribution.
Answer: InvNormal(0.60, 65, 3.4)= 65.86138014
b)_ 65.86138014__
8. The grades for a large statistics class are normally distributed with mean of 64 and a standard
deviation of 15.3. If the middle 40% of the class will receive C's in the exam, what are the lowest and
highest C grade.
Give answer rounded to one decimal place.
Lowest C=55.9
Lowest C = invNormal (0.30, 64, 15.3) =55.9766722
8.__Highest C= 72.0___________
Highest C = invNormal (0.70, 64, 15.3) =72.0233278
9. In January 21, 1938, the temperature in San Fernando de la Torres was normally distributed with mean of 34
degrees and standard deviation of 2.5 degrees. What percentage of the time was the temperature above
freezing, that is above 32 degrees Fahrenheit?
Normalcdf(32, 10^9, 34, 2.5) = 0.7881446663
9. __78.81%______________
10 5% of the production of a certain company is rejected due to too much alcohol, and has to be re-processed.
It is known that the standard deviation for the milliliters of alcohol per bottle is 0.4 and that if a bottle contains
more than 5 milliliters of alcohol, it is rejected. What is the average amount of alcohol per bottle?
MATH 0  CLEAR
ALPHA SOLVE
X=4.3420586099
eqn: 0= normalcdf ( 5, 10^9, x, 0.4) - 0.05
ENTER x=make a good guess
10.____average is 4.34 milliliters per bottle. _
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