Question 1
A package delivery service claims that no more than 5 percent of all packages arrive at the address late. Assuming that the conditions for the binomial hold, if a sample of size 10 packages is randomly selected and the 5 percent rate holds, what is the probability that more than 2 packages will be delivered late?
Question 2
A package delivery service claims that no more than 5 percent of all packages arrive at the address late. Assuming that the conditions for the binomial hold, if a sample of size 10 packages is randomly selected, and the 5 percent rate holds, what is the probability that exactly 2 packages in the sample arrive late?
Question 3
A sales rep for a national clothing company makes 4 calls per day. Based on historical records, the following probability distribution describes the number of successful calls each day:
Based on this information, the probability that the sales rep will have a total of 2 successful calls in a two-day period is:
Question 4
A sales rep for a national clothing company makes 4 calls per day. Based on historical records, the following probability distribution describes the number of successful calls each day:
The expected number of successful sales calls per day is:
Question 5
A sales rep for a national clothing company makes 4 calls per day. Based on historical records, the following probability distribution describes the number of successful calls each day:
Based on the information provided, what is the probability having at least 2 successful calls in one day?
Question 6
Assuming that potholes occur randomly along roads, the number of potholes per mile of road could best be described by the:
Question 7
Consider the following two probability distributions:
Which of the following is an accurate statement regarding these two distributions?
Question 8
If cars arrive to a service center randomly and independently at a rate of 5 per hour on average, what is the probability of 0 cars arriving in a given hour?
Question 9
If cars arrive to a service center randomly and independently at a rate of 5 per hour on average, what is the probability that exactly 5 cars will arrive during a given hour?
Question 10
If the number of defective items selected at random from a parts inventory is considered to follow a binomial distribution with n = 50 and p = 0.10, the expected number of defective parts is:
Question 11
If the number of defective items selected at random from a parts inventory is considered to follow a binomial distribution with n = 50 and p = 0.10, the standard deviation of the number of defective parts is:
Question 12
If the standard deviation for a Poisson distribution is known to be 3, the expected value of that Poison distribution is:
Answer
Question 13
Madam Helga claims to be psychic. A national TV talk personality plans to test her in a live TV broadcast. The process will entail asking Madam Helga a series of 20 independent questions with yes/no answerers. The questions would be of the nature that she could not have any way of knowing the answer from prior knowledge. Suppose that Madam Helga correctly answered 15 of the 20 questions, which of the following would be a viable conclusion to reach?
Answer
Because the probability of guessing 15 or more correctly is 0.0207, it is unlikely that she is guessing at the questions and may, in fact, have some special ability.
Because the probability of getting 15 or more correct is 0.0207, it is likely that she is just guessing at the questions.
If she were guessing, 15 is within one standard deviation of the mean and therefore she must not have any special psychic abilities.
Because the probability of guessing exactly 15 correct is 0.0148, she must just be guessing.
Question 14
Madam Helga claims to be psychic. A national TV talk personality plans to test her in a live TV broadcast. The process will entail asking Madam Helga a series of 20 independent questions with yes/no answers. The questions would be of the nature that she could not have any way of knowing the answer from prior knowledge. She will be considered psychic if she correctly answers more than a specified number (called the cut-off) of the questions. The cut-off must be set so that the chance of guessing that number or more is no greater than 5 percent. The cut-off value should be:
Question 15
Many people believe that they can tell the difference between Coke and Pepsi. Other people say that the two brands can't be distinguished. To test this, a random sample of 20 adults was selected to participate in a test. After being blindfolded, each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was. If people really can't tell the difference, the expected number of correct identifications in the sample would be:
Question 16
Many people believe that they can tell the difference between Coke and Pepsi. Other people say that the two brands can't be distinguished. To test this, a random sample of 20 adults was selected to participate in a test. After being blindfolded, each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was. If people really can't tell the difference, the probability that fewer than 6 people will guess correctly is:
Question 17
Many people believe that they can tell the difference between Coke and Pepsi. Other people say that the two brands can't be distinguished. To test this, a random sample of 20 adults was selected to participate in a test. After being blindfolded, each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was. Suppose 14 people correctly identified the soft drink brand. Which of the following conclusions would be warranted under the circumstance?
Answer
Since the chance of getting 14 correct is 0.0370, which is quite small, the study shows that people are not able to identify brands effectively.
Since the probability of getting 14 or more correct is 0.0577, which is quite low, this means that people are not effective in identifying the soft drink brand.
Since the probability of getting 14 or more correct is 0.0577, which is quite low, the conclusion could be that people are effective at identifying soft drink brands.
The expected value for this binomial distribution is very close to 14 so this supports that people cannot tell the difference.
Question 18
Previous research shows that 60 percent of adults who drink non-diet cola prefer Coca-Cola to Pepsi. Recently, an independent research firm questioned a random sample of 25 adult non-diet cola drinkers. That chance that 20 or more of these people will prefer Coca-Cola is:
Question 19
The Vardon Exploration Company is getting ready to leave for South America to explore for oil. One piece of equipment requires 10 batteries that must operate for more than 2 hours. The batteries being used have a 15 percent chance of failing within 2 hours. The exploration leader plans to take 15 batteries. Assuming that the conditions of the binomial apply, the probability that the supply of batteries will contain enough good ones to operate the equipment is:
Question 20
The Vardon Exploration Company is getting ready to leave for South America to explore for oil. One piece of equipment requires 10 batteries that must operate for more than 2 hours. The batteries being used have a 15 percent chance of failing within 2 hours. The exploration leader plans to take 15 batteries. Assuming that the conditions of the binomial apply, the probability that the supply of batteries will not contain enough good ones to operate the equipment is:
Question 21
The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day:
The probability of having less than 2 accidents on a given day is:
Question 22
The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day:
Based on this distribution, the expected number of accidents in a given day is:
Question 23
The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day:
Based on this probability distribution, the standard deviation in the number of accidents per day is:
Question 24
The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that 2 or 3 customers will arrive in a 15-minute period?
Question 25
The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that no customers will arrive in a 15-minute period?
Question 26
The number of weeds that remain living after a specific chemical has been applied averages 1.3 per square yard and follows a Poisson distribution. Based on this, what is the probability that a 3-square yard section will contain less than 4 weeds?
Question 27
The probability that a product is found to be defective is 0.10. If we examine 50 products, which of the following has the highest probability?
Question 28
A quiz has 20 multiple-choice questions. Each question has 4 answer options (A, B, C, and D). Pat is unprepared for the quiz and guesses on every question. To pass the quiz, Pat must answer at least 12 questions correctly. What is the probability Pat will pass the quiz?