Question
MATH399 Applied Managerial Statistics
Week 4 Assignment Distribution with Technology – Excel
QuestionAbaseball 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
downloaded 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 downloaded 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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