DEVRY MATH399 Week 4 Assignment Distribution with Technology – Excel Latest 2019 JULY
MATH399 Applied Managerial Statistics
Week 4 Assignment Distribution with Technology
– Excel
QuestionA
baseball park ran a “$1 Hot Dog Night” promotion. The average number of hot
dogs purchased that night was 3.3 hot dogs per fan. Find the probability that a
randomly selected fan who attended $1 Hot Dog Night purchased 5 or more hot
dogs.
• Round your answer to 3 decimal
places.
QuestionIn
baseball, the statistic Walks plus Hits per Inning Pitched (WHIP) measures the
average number of hits and walks allowed by a pitcher per inning. In a recent
season, Burt recorded a WHIP of 1.315. Find the probability that, in a randomly
selected inning, Burt allowed a total of 3 or more walks and hits. Use Excel to
find the probability.
• Round your answer to three decimal
places.
QuestionA
steel mill manufactures steel plates. The average number of flaws in the steel
is 1.28 flaws per square foot. Find the probability that a randomly selected
1-foot-by-1-foot area of steel plate has 2flaws or fewer. Use Excel to find the
probability.
• Round your answer to three decimal
places.
QuestionAlex
wants to test the reliability of “lie detector tests,” or polygraph tests. He
performs a polygraph test on a random sample of 12 individuals. If there is
more than a 50% chance that the tests result in no false positives (that is,
the test does not result in a true statement being recorded as a lie), Alex
will conclude that the tests are reliable. If the probability of a lie detector
test resulting in a false positive is 5.5%, what will Alex conclude? Use Excel
to find the probability, rounding to three decimal places.
Alex will
conclude that the test is reliable since the probability of no false positives
is less than 0.5.
Alex will conclude that the test is not
reliable since the probability of no false positives is greater than 0.5.
Alex will conclude that the test is not
reliable since the probability of no false positives is less than 0.5.
Alex will conclude that the test is reliable
since the probability of no false positives is greater than 0.5.
QuestionAt
a certain fast food restaurant, 77.5% of the customers order items from the
value menu. If 14customers are randomly selected, what is the probability that
at least 9 customers ordered an item from the value menu? Use Excel to find the
probability.
• Round your answer to three decimal
places.
QuestionA
survey asked parents of children aged ten and under how many birthday parties
they attended last year. Let X represent the number of birthday parties. The
probability distribution is given below. Find the mean and the standard
deviation of the probability distribution using Excel.
• Round the mean and standard
deviation to three decimal places.
QuestionTo
see if a spinner that is divided into 100 equal sections labeled 1 to 100 is
fair, a researcher spins the spinner 1000 times and records the result. Let X
represent the outcome. The table below shows the probability distribution of
the data. Find the mean and the standard deviation of the probability
distribution using Excel.
• Round the mean and standard
deviation to two decimal places.
QuestionIn
a recent baseball season, Ron was hit by pitches 24 times in 633 plate
appearances during the regular season. Assume that the probability that Ron
gets hit by a pitch is the same in the playoffs as it is during the regular
season. What is the probability that Ron gets his first hit-by-pitch of the
playoffs in his first 16 plate appearances? Use Excel to find the probability.
• Round your answer to three decimal
places.
QuestionBurt,
a football quarterback, has a pass completion percentage of 55.2%. If the probability
that Burt will need 8 or more pass attempts to complete his first pass in a
game is at least 0.01, then Burt will be benched and replaced by a backup. Will
Burt be benched? Use Excel to find the probability, rounding to three decimal
places.
Burt will
not be benched since the probability is less than 0.01.
Burt will be benched since the probability is
less than 0.01.
Burt will be benched since the probability is
at least 0.01.
Burt will not be benched since the probability
is at least 0.01.
QuestionAn
insurance company is assessing the risk of selling flood insurance. Under the
company’s policies, if a customer lives in an area where they have a greater
than 5% chance of experiencing 4 or more floods in 10 years, the customer must
pay a higher premium. Drew lives in an area where the average number of floods
per 10 years is 1.6 floods. Will Drew have to pay the higher premium for flood
insurance? Use Excel to find the probability.
Drew will
not have to pay the higher premium because the probability is greater than
0.05.
Drew will have to pay the higher premium
because the probability is less than 0.05.
Drew will not have to pay the higher premium
because the probability is less than 0.05.
Drew will have to pay the higher premium
because the probability is greater than 0.05.
QuestionIn
a 40-year period, a city’s official weather station recorded 78 snowstorms with
at least 12 inches of total snow accumulation. Assume that this pattern follows
a Poisson distribution. Find the probability that the city’s weather station
records exactly 4 snowstorms with at least 12 inches of total snow accumulation
for one randomly selected year in the period. Use Excel to find the
probability.
• Round your answer to three decimal
places.
QuestionSuppose
your favorite celebrity posts an average of 2.3 messages per day on a
particular social media website. Find the probability that she posts exactly
one message for any random day.
• Round your answer to three decimal
places.
Create and
Interpret a Poisson Distribution With Excel
Finding
Poisson Probabilities Using Excel
A Poisson
distribution can be used to represent the number of occurrences of an event
that take place within a specific time period or area. Excel can be used to
find a probability from a Poisson probability distribution instead of using a
formula to compute individual probabilities. Excel can find probabilities from
a probability density function or a cumulative probability. The probability
density function gives the probability that the random variable is equal to
some given individual value, whereas the cumulative probability function gives
the probability that the random variable is less than or equal to some given
individual value.
For example, let’s suppose that the mean
number of phone calls you receive per week from an unknown number is 10. For
any random week, suppose we want to determine the probability that you receive
exactly 5 calls from an unknown number.
Key Terms
• Poisson Distribution: a discrete
probability distribution that gives the probability of a number of events
occurring in a fixed interval of time or space
How To
Find a
Poisson Probability with Excel
To
determine the probability from a Poisson distribution using Excel, follow the
steps below.
1. First
press FORMULAS and then INSERT FUNCTION.
An Excel
toolbar has tab Formulas selected and the first button from the left labeled f
x Insert Function is circled.
2. Then select the POISSON.DIST function.
3. Next
enter the values for the number of events and the mean or the expected number
of occurrences per interval. In this case, enter 5 and 10, in that order. Enter
0 for Cumulativesince this is not a cumulative probability.
An Excel dialog box for the Poisson dot DIST
function has the following function argument entries from top to bottom, where
the label is listed first and the entry is listed second: X, 5; Mean, 10;
Cumulative, 0.
4. Press OK. Excel should then display the
probability. Here, the resulting probability is 0.037833.
Note: The
last entry would be a 1 to find a cumulative probability.
Example
Question:An
animal rescue organization computes that there are an average of 8.2 feral cats
per acre of uninhabited land in a certain city. Find the probability that there
are fewer than 6feral cats living on a random acre of uninhabited land in the
city.
QuestionIn a recent basketball season, a team
scored 107.7 points per 100 possessions. Find the probability that, in a
randomly selected interval of 100 possessions, the team scored exactly 112
points. Use Excel to find the probability.
• Round your answer to three decimal
places.
QuestionA
database system assigns a 32-character ID to each record, where each character
is either a number from 0 to 9 or a letter from A to F. Assume that each number
or letter being selected is equally likely. Find the probability that at least
20 characters in the ID are numbers. Use Excel to find the probability.
• Round your answer to three decimal
places.
QuestionA
data scientist tracks the number of songs that are ed from a particular
website over the course of a year. She uses the data to build a probability
distribution where the random variable Xrepresents the number of songs
ed per person each day. The distribution is given below. Find the mean
and the standard deviation of the probability distribution using Excel.
• Enter the mean and round the
standard deviation to three decimal places.
QuestionA
soda bottling company’s manufacturing process is calibrated so that 99% of
bottles are filled to within specifications, while 1% is not within
specification. Every hour, 12 random bottles are taken from the assembly line
and tested. If 2 or more bottles in the sample are not within specification,
the assembly line is shut down for recalibration. What is the probability that
the assembly line will be shut down, given that it is actually calibrated
correctly? Use Excel to find the probability.
• Round your answer to three decimal
places.
QuestionA
stock exchange computes that there is an average of 2.7 initial public
offerings (IPOs) per week on the exchange. Find the probability that there are
5 IPOs in a randomly selected week. Use Excel to find the probability.
• Round your answer to three decimal
places.
QuestionKatie
handles calls for a company’s information technology help desk, either by
resolving the issue herself or forwarding the call to the appropriate team.
About 12.9% of the help desk calls need to be forwarded to another team. What
is the probability that the first call Katie needs to forward to another team
will be one of the first seven calls she receives that day? Use Excel to find
the probability.
• Round your answer to three decimal
places.
QuestionAlison
is playing a racing video game, in which she can pick up items from item boxes.
One of the possible items is a speed booster, which has a 1 in 12 chance of
appearing in any item box. What is the probability that Allison will get her
first speed booster in one of her first five item boxes? Use Excel to find the
probability.
• Round your answer to three decimal
places.
QuestionAn
automobile manufacturer is concerned about the possibility of a fault in the
engine of a particular model of one of its cars. This fault could potentially
cause the engine to fail to start. The average number of cars per year that
experience this fault is 3 cars. If the probability that 8 or more cars
experience this fault in a year is greater than 0.05, the company will issue a
recall. Will the company issue a recall for this engine fault? Use Excel to
find the probability.
The company
will not issue a recall because the probability is less than 0.05.
The company
will not issue a recall because the probability is greater than 0.05.
The company will issue a recall because the
probability is greater than 0.05.
The company
will issue a recall because the probability is less than 0.05.
QuestionA
study randomly selected 100 samples, each of which consisted of 100 people, and
recorded the number of left-handed people, X. The table below shows the
probability distribution of the data. Find the mean and the standard deviation
of the probability distribution using Excel.
• Round the mean and standard
deviation to two decimal places.
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