Binomial Distribution Probability

A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately 1/4 of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item?

Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange. Two independent random samples, each of size 25, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies. The total number of orange candies in the two samples is observed. What are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples?

• 7 and 2.905

• 7 and 3.987

• 13.75 and 2.233

• 13.75 and 2.905

• 13.75 and 3.987

The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?

• n=10 only

• n=20 only

• n=100 only

• n=10 or n=20 only; the probabilities are the same.

• n=10 or n=20 or n=100 ; the probabilities are the same.

A popular computer card game keeps track of the number of games played and the number of games won on that computer. The cards are shuffled before each game, so the outcome of the game is independent from one game to the next and is based on the skill of the player. Let X represent the number of games that have been won out of 100 games. Under which of the following situations would X be a binomial random variable?

• All games were played by the same player, whose skill improved over the course of the 100 games

• A group of 5 players of different skill levels were each allowed to play 20 games in a row.

• A group of players of different skill levels were each allowed to play until they had lost 3 games and this resulted in 100 games played.

• Two players of equal skill level each played one game a day for 50 days and their skill level did not change from day to day.

• Two players of different skill levels competed by allowing one player to continue until a game was lost, then the other player to continue until a game was lost, and so on, until 100 games were played.

It is known that 75 percent of all households in the United States have intermittent Internet connectivity problems. For random samples of 450 independent households in the United States, what are the mean, μ, and standard deviation, σ, of the distribution of the number of households that have intermittent Internet connectivity problems?

Suppose 39% of Americans will vote for Donald Trump on election day. If a random sample of 8 voters are selected, what is the probability that 6 or more will vote for Trump?

• .9635

• .0365

• .9561

• .0439

A survey found that 25% of pet owners had their pets bathed professionally rather than do it themselves. If 18 pet owners are randomly selected, find the probability that exactly 5 people have their pets bathed professionally

• 3.42

• 1.03

• 0.072

• 0.199

A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what is the probability that at least one tie is too tight?

• 27.0%

• 12.2%

• 73.0%

• 87.8%

The student who makes the morning announcements has the bad habit of saying “like” all the time. The chance that they say “like” in a sentence is 60%. You decide to keep a tally of how many times they say like. If they say 350 sentences this week, what is the probability that they will say “like” at least 200 times?

• 0.87

• 0.13

• 0.85

• 0.15

If you were to flip a coin 20 times, what is the probability you would get at most 13 heads?

• .9423

• .1316

• .0577

• .0739