Download It`s here! Practice Problems for Exam 2

Community College of Denver
Course: MAT135 –Statistics
Instructor: Vikki French
[email protected]
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Practice Problems for Exam 2
1) In a 1 pound bag of skittles the possible colors were red, green, yellow, orange, and
purple. The probability of drawing a particular color from that bag is given below.
(You must show your work to get credit)
Color
Probability
Red
Green
Orange
Yellow
Purple
0.1764
0.2109
?
0.1045
0.3055
a. (1 pt) What is the probability of selecting an Orange skittle?
b. (1 pt) What is the probability of not selecting a Yellow skittle?
c. (1 pt) What is the probability of selecting a Red or Green skittle?
d. (1 pt) What is the probability of selecting a Blue skittle?
e. (1 pt) What skittle color is the most likely?
f. (1 pt) Give the expected value the skittle color using the discrete probability
distribution above.
2) A study was recently done that emphasized the problem we all face with drinking
and driving. Four hundred accidents that occurred on a Saturday night were
analyzed. Two items noted were the number of vehicles involved and whether
alcohol played a role in the accident. The numbers are shown below:
Frequencies:
Did alcohol play a role?
Yes
No
Number of Vehicles Involved
1
2
3
51
98
21
30
175
25
Suppose we Randomly select 1 accident from the table above:
(You must show your work to get credit)
a. (6 pt) Complete the probability table:
Probabilities:
Did alcohol play a role?
Yes
No
1
Number of Vehicles Involved
2
3
b. (1 pt) What is the probability that alcohol played a role and 2 cars were
involved?
c. (1 pt) What is the probability that 1 car was involved?
d. (1 pt) What is the probability that alcohol didn’t play a role?
e. (1 pt) What is the probability that alcohol didn’t play a role or three cars were
involved?
f. (1 pt) What is the probability that at most 2 cars were involved?
g. (1 pt) Given that alcohol played a role, what is the probability that 1 car was
involved?
3) You have 27 songs on your MP3 player and randomly select one to play. One song
is your favorite.
Give the probability of the indicated event:
(You must show your work to get credit)
a. (1 pt) What is the chance that your favorite song will be the one to play?
b. (2 pts) When it finishes, you again randomly select a song to play, and it’s
the same one! What is the chance of this happening (2 in a row)?
c. (2 pts) When it finishes, you again randomly select a song to play, and it’s
the same one! What is the chance of this happening (3 in a row)?
4) Based on data from a survey of college campuses, 46% of students drink energy
drinks. 5 college students are selected randomly. (You must show your work to
get credit)
a. (1 pt) What is "success"?
b. (1 pt) What is n?
c. (1 pt) What is p?
d. (1 pt) What is q?
e. (7 pts) The probability distribution is (remember P(x) = nCx px(q)n-x):
0
1
2
3
4
5
6
f. (1 pt) Give the mean of this binomial distribution:
g. (1 pt) Give the standard deviation of this binomial distribution: (use √𝑛𝑝𝑞)
h. (1 pt) Compute the z-score for the outcome x = 0 people who say they do not
drink energy drinks:
5) In a court case, a jury pool of 100 people was randomly selected from population in
which 51% of the citizens were females.
(You must show your work to get credit)
a. (1 pt) What is n?
b. (1 pt) What is p?
c. (1 pt) What is the expected proportion of females in the jury pool (the mean)?
d. (1 pt) What is the standard error of the proportion of females in the jury pool?
𝑝𝑞
(use √ 𝑛 )
e. (1 pt) What is the probability that a jury pool of 100 people will have exactly
20 females? (remember P(x) = nCx px(q)n-x)
f. (1 pt) What is the probability that a jury pool of 100 people will be have 10 or
fewer females? (Hint: can this binomial be approximated using the normal
distribution?)
g. (1 pt) What is the probability that none of the people in the jury pool are
females?
h. (1 pt) What is the probability that a jury pool of 100 people will have between
15 and 30 females?
6) The height of female Martians are normally distributed with a mean
height of 26.5 inches and a standard deviation of 1.4 inches, while Martian males
have a mean height of 24.4 inches and a standard deviation of 1.2 inches.
(You must show your work to get credit)
a. (2 pts) Martian buildings typically have doors that are 28 inches high. What
percent of Martian females are taller than that?
b. (2 pts) What percent of Martian males are shorter than 28 inches?
c. (2 pts) If Martian doors were changed so that 95% of females would be
shorter that the height of the doors, what would the new height of Martian
doors?
d. (2 pts) Martina is in the 95th percentile for females. Is she shorter than the 28inch height of the standard door?
e. (2 pts) The Martian Space Force requires that their pilots be between 25 and
27.5 inches tall in order to operate their spacecraft. What percent of females
are within those limits?
f. (2 pts) If the Martian Space Force redesigned its craft to fit the middle 95%
of females, what would the cutoff heights be?
7) A brewery has a filling machine that fills 12 ounce bottles of beer. The amount of
beer poured by this filling machine follows a normal distribution with a mean of 12
ounces and a standard deviation of 0.04 ounce. Quality control sets upper and lower
limits on the acceptable variation in the amount poured. If there are too many high or
low values, the range of acceptable weights can be modified.
(You must show your work to get credit)
a. (1 pt) If the machine is set to allow fillings between 11.95 g and 12.05 g, what
percent of fillings are being rejected?
b. (1 pt) Is this percentage too high? Explain.
c. (1 pt) If you wanted to reject only 3% of the fillings, what would you set as
your upper and lower limits on the machine?
8) The weight of a mature cardinal is normally distributed with a mean of 78 grams and
a standard deviation of 7.4 grams. 90% of all Cardinals are between what two
weights?
(You must show your work to get credit)
a. (2 pts) 10% of cardinals die because their weight is below a minimum. What
value is this minimum?
b. (2 pts) 5% of cardinals die because their weight is above a maximum. What
value is this maximum?
c. (2 pts) What percent of cardinals are less than 83 g?