STAT 202162-Explain why this is an example of a binomial random
Question # 00396384
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Updated on: 09/28/2016 12:30 AM Due on: 09/28/2016
2. Use Minitab Express to answer the following set of questions. Be sure to include all
relevant output and clearly identify your answers by writing a sentence. A student is
conducted an experiment in which he is randomly selecting a card from a standard 52card deck, records if the card is a heart or not, puts the card back in the deck, and
repeats 5 more times (i.e., he pulls a total of 6 cards in each experiment).
A. Explain why this is an example of a binomial random variable.
B. What are the values of the parameters n and p?
C. What is the mean number of hearts pulled across many 6 trial experiments?
D. What is the standard deviation of the number of hearts pulled across many 6
trial experiments?
E. What is the probability that the results of 6 out of 6 trials are hearts?
F. What is the probability of pulling more than 2 hearts out of 6 trials?
3. Your friend is in a casino for the first time and he decides to play some American
roulette. First, he bets $10 on red and he wins! Then, he bets $10 on red again and he
wins again! Use this information to answer the following questions.
If you use Minitab Express, copy + paste your output along with an explanation.
For a table of roulette betting odds see:
https://en.wikipedia.org/wiki/Roulette#Bet_odds_table.
Note that this is American roulette with 38 slots: 18 red, 18 black, and 2 green.
A. If your friend plays a third round and bets $10 on red, what is the probability
that he will win that round?
B. If an individual plays three rounds of American roulette, what is the
probability that he or she will win all three times?
C. Your friend’s friend joins him at the casino and she plays 3 games of roulette,
betting $10 on red each time. What is the probability that she will finish with
more money than she started with? (Hint: When you bet on red and win you
get your $10 bet back plus an additional $10, if you lose you lose your $10 bet)
D. Assume that both of these individuals made money during their first short
trip to the casino. How are casinos making money if two people can walk in
and come out with more money? Apply what you have learned about
probability distributions in this lesson. It is expected that about 50-75 words
will be needed to fully answer this question.
4. You are in charge of ordering t-shirts for children for an event. The shirts are
available in small, medium, and large. Small shirts fit children up to 45 pounds.
Medium shirts fit children 45-60 pounds. Large shirts fit children 60-110 pounds. The
distribution of the weights of the children who are attending this event has a mean of
56 pounds with a standard deviation of 14 pounds. You are expecting 200 children at
the event. How many t-shirts of each size should you order? Be sure to include all
relevant Minitab Express output and clearly identify your answers by writing a
sentence.
Extra Credit
Total Graduate Management Admissions Test (GMAT) scores range from 200 to 800 in
10 point intervals with a mean of 545.6 and standard deviation of 121.07. The
program that you want to enroll in requires a total GMAT score in the top 5% of the
population. What is the minimum GMAT score that you need to obtain to be
admitted?
relevant output and clearly identify your answers by writing a sentence. A student is
conducted an experiment in which he is randomly selecting a card from a standard 52card deck, records if the card is a heart or not, puts the card back in the deck, and
repeats 5 more times (i.e., he pulls a total of 6 cards in each experiment).
A. Explain why this is an example of a binomial random variable.
B. What are the values of the parameters n and p?
C. What is the mean number of hearts pulled across many 6 trial experiments?
D. What is the standard deviation of the number of hearts pulled across many 6
trial experiments?
E. What is the probability that the results of 6 out of 6 trials are hearts?
F. What is the probability of pulling more than 2 hearts out of 6 trials?
3. Your friend is in a casino for the first time and he decides to play some American
roulette. First, he bets $10 on red and he wins! Then, he bets $10 on red again and he
wins again! Use this information to answer the following questions.
If you use Minitab Express, copy + paste your output along with an explanation.
For a table of roulette betting odds see:
https://en.wikipedia.org/wiki/Roulette#Bet_odds_table.
Note that this is American roulette with 38 slots: 18 red, 18 black, and 2 green.
A. If your friend plays a third round and bets $10 on red, what is the probability
that he will win that round?
B. If an individual plays three rounds of American roulette, what is the
probability that he or she will win all three times?
C. Your friend’s friend joins him at the casino and she plays 3 games of roulette,
betting $10 on red each time. What is the probability that she will finish with
more money than she started with? (Hint: When you bet on red and win you
get your $10 bet back plus an additional $10, if you lose you lose your $10 bet)
D. Assume that both of these individuals made money during their first short
trip to the casino. How are casinos making money if two people can walk in
and come out with more money? Apply what you have learned about
probability distributions in this lesson. It is expected that about 50-75 words
will be needed to fully answer this question.
4. You are in charge of ordering t-shirts for children for an event. The shirts are
available in small, medium, and large. Small shirts fit children up to 45 pounds.
Medium shirts fit children 45-60 pounds. Large shirts fit children 60-110 pounds. The
distribution of the weights of the children who are attending this event has a mean of
56 pounds with a standard deviation of 14 pounds. You are expecting 200 children at
the event. How many t-shirts of each size should you order? Be sure to include all
relevant Minitab Express output and clearly identify your answers by writing a
sentence.
Extra Credit
Total Graduate Management Admissions Test (GMAT) scores range from 200 to 800 in
10 point intervals with a mean of 545.6 and standard deviation of 121.07. The
program that you want to enroll in requires a total GMAT score in the top 5% of the
population. What is the minimum GMAT score that you need to obtain to be
admitted?
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Solution: STAT 202162-Explain why this is an example of a binomial random