Binomial and Geometric Quiz

Which of the following is true about geometric distributions?

• Geometric distributions are approximately skewed right.
• Geometric distributions are approximately symmetric.
• Geometric distributions are approximately skewed left.
• The shape could be symmetric or skewed.

Which of the following is false about binomial probabilities?

• Their distributions are approximately symmetric.
• Trials must be fixed.
• Events musts be independent.
• The probability of success must be 0.50

When rolling a fair die 100 times, what is the probability of rolling a "4"exactly 25 times?

• 0.010
• 0.167
• 0.25
• 0.021

At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds.  Find the probability that out of the next eight eastbound cars that arrive randomly at the light,exactly three will be stopped by a red light.

• 0.254
• 0.147
• 0.027
• 0.1940

The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4% of the customers buy specialty clothes for their pets. What is the probability that she does NOT sell a garment until the 7th customer? Assume each customer is independent.

• 0.033
• 0.027
• 0.0313
• Not here

Which one of these variables is a continuous random variable?

• The time it takes a randomly selected student to complete an exam.
• The number of tattoos a randomly selected person has.
• The number of women taller than 68 inches in a random sample of 5 women. 
• The number of correct guesses on a multiple choice test. 

Which one of these variables is a continuous random variable?

• The time it takes a randomly selected student to complete an exam.
• The number of tattoos a randomly selected person has.
• The number of women taller than 68 inches in a random sample of 5 women. 
• The number of correct guesses on a multiple choice test. 

The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy a magazine and thinks that he might be able to use the display space to sell something more profitable. What is the probability that at least 5 of his first 50 customers buy magazines?

• 0.104
• 0.896
• 0.066
• 0.774

Which one of these variables is a binomial random variable?

• Time it takes a randomly selected student to complete a multiple choice exam
• Number of textbooks a randomly selected student bought this term 
• Number of women taller than 68 inches in a random sample of 5 women
• Number of CDs a randomly selected person owns

Suppose that a quiz consists of 20 True-False questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with True and False equally likely). How would you find the probability that the will student get 8 or fewer answers correct? √

• Find the probability that X=8 in a binomial distribution with n = 20 and p=0.5. 
• Find the area between 0 and 8 in a uniform distribution that goes from 0 to 20. 
• Find the probability that X=8 for a normal distribution with mean of 10 and standard deviation of √5
• Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.