Solution
Approximately 73% of Americans artificial intelligence= 73% = 0.73; or 0.27
Random sample of Americans = 30
1.
A professor gives a twenty question true/false quiz.
The lowest passing quiz score is 12 correct out of 20. Suppose a student randomly and independently
guesses on each quiz question, what is the probability that the student earns a
passing grade? Round to 4 decimal
places.
Solution
Lowest passing quiz score is =
Professor gives a question true/false quiz = 20 questions
2.
When commercial aircrafts are inspected, wing cracks
are reported as nonexistent, detectable, or critical. The history of a
particular fleet indicates that 75% of the planes inspected have no wing
cracks, 22% have detectable wing cracks, and 3% have critical wing cracks.
Eight planes are randomly selected. Find the probability that five have no
cracks, two has detectable cracks, and one has critical cracks. Round to 4 decimal places.
Solution
We have commercial aircraft
are inspected; wing cracks are reported as nonexistent, detectable, or
critical. Here the 75% of the planes inspected have no wing cracks, 22% have
detectable wing cracks and 3% have critical wing cracks. Eight planes are
randomly selected.
Here our goal is:
A). we need to find probability that five have no cracks, two has
detectable cracks, and one has critical cracks.
a).
Here we have:
The number of aircraft have
critical crack = 1,
The number of aircraft have
detectable cracks = 2, and
The number of aircraft have
no cracks = 5.
3.
In an Elementary school, there are 5 students with
autism, 8 students with emotional disabilities, and 3 students with learning
disabilities. A researcher is going to randomly select 6 of these students to
participate in a small study.
a.
What is the probability that the
researcher selects 2 students with autism, 3 students with emotional
disabilities, and 1 student with learning disabilities? (Do not simplify your answer)
Solution
b.
What is the probability that the researcher selects at
least 1 student with emotional disabilities? (Do not simplify your answer)
Solution
Researcher selects at least 1 student
with emotional disabilities
c.
(2 points) How many students with
emotional disabilities are expected to be selected for the study?
Solution
d.
(2 points) Calculate the variance for the number of emotional
disability students who are selected to participate in the study.
Solution
4.
The 1990 board game Key to the Kingdom uses a
green 8-sided die. When playing a quick game, a player wins by finding
the Key and one other treasure then rolling an 8. Assume a player has found the
Key and one other treasure.
a.
Find the probability that the player rolls a number 8
on their fifth turn.
Round to 4 decimal places
Solutio
b.
(2 points) What is the expected number of rolls for the player to
roll a number 8?
Solution
5. Find the probability that a person rolling a standard 6-sided die
rolls a third number 4 on the twelfth roll. Round to 4 decimal places.
Solution
6. (1 point each) Assume a continuous random variable X has a
continuous uniform distribution between 92 and 98. Find the following:
a.
The height of the uniform distribution.
7.
The number of typos by a typist follows a Poisson
process with an average of 1 typo per 300 words. A typical page contains 300
words. Let X be the number of defects per page.
a.
Find the probability that one page (300 words)
contains three typos.
b.
(2 points) A proposal has a 225 word
limit. Let Y be the
number of typos in the proposal (225 words). Find E(Y) = µ.
c.
Find
the probability that the proposal of 225 words contains at most two typos.
9. Find the
area under the standard normal distribution curve to the right of Z = 0.57.
Form the
standard normal distribution table
Curve to the
right of Z = 0.57
So area is = 
10. A certain
brand of thermometers measures the freezing point of water with a mean of 0ºC and a standard deviation of 1ºC.
Assume the readings are normally distributed. Find the probability that a
randomly selected thermometer reads the freezing point of water as less than –
2.77ºC or higher than 1.89ºC.
If one thermometer
is randomly selected, find the probability that, at the freezing point of
water, the reading is between –2.77 ºC and 1.89ºC
12. Find the two
Z values that separate the middle 87% of the standard normal distribution.
13. Police officer exams
have an average score of 79 with a standard deviation of 4.5. Assume police
officer exam scores follow a normal distribution.
a.
What is the minimum score a recruit needs to be in the
top 10% on the exam?
14. Time spent per day on cellphones is normally distributed with a mean of
3.25 hours and a standard deviation of 0.55 hours. What is the probability that
a randomly selected person spends between 3 and 4.5 hours on their cellphone
that day?
15. For a
lottery scratcher, 1 in 5 tickets sold will win a prize. Suppose a local
convenience store has sold 144 of these scratcher tickets. What is the
probability that at most 36 of them won prizes? Use the Normal Approximation to a Binomial.
16. The life of a certain brand of tires is normally distributed with an
average life of 60,000 miles with a standard deviation of 3,750 miles.
a. Find the
probability that the mean life of 30 randomly selected tires is between 58,000
miles and 61,000 miles.
b. Find the
mileage life of tires for which 20% of the sample means computed from random
samples of 30 would fall above. (Round to
2 decimal places.)
17. (2 pts each) Let χ2 denote a random variable that has a chi-square
distribution with 15 degrees of freedom. Determine the following
a. P (7.261 ≤ χ2 ≤ 11.721)
P (7.261 ≤ χ2 ≤ 11.721)
P (0.95 ≤ χ2 ≤ 0)
b. The limit
c such that P( χ2 ≥ c ) = 0.025
P( χ2 ≥ c ) = 0.025
P( χ2 ≥ c )
= 27.488
18. (2 pts each) Let T have a t distribution
with 10 degrees of freedom. Determine a. P(
T ≤ 1.812 )
19. (2
pts each) Let F(6, 15) denote a random variable having an F distribution with ν1 = 6
and
ν2 =15.
a.
a. P( F(6,
15) ≥ 2.79)
b.
The limit c such
that P( F(6, 15)
< c ) = 0.01. (Round to 4 decimal places)
