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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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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