Chap 6 connect readings
The Dean's secretary receives an average of 3 calls per hour. Assuming the Poisson distribution applies, what is the probability that the secretary will receive 6 calls next hour?
0.050
A software salesman knows that on average he will make one sale for every ten companies he calls. Let "success" be making a sale. (P(success)=0.10) Use binomial probability formula to find the chance that he will make two sales if he calls 6 companies.
0.098
On average, 12 customers use the bank's ATM during the noon lunch hour. What is the probability that exactly 10 customers will use the ATM during the next noon lunch hour? Assume the Poisson distribution applies.
0.105
The table shown provides binomial probabilities for n=10. If 30% of adults take a vacation each year, what is the probability that four of 10 randomly sampled adults would indicate they take a vacation every year?
0.200
A grocery store employee checks 200 apples and finds that 8 are spoiled. On average, how many apples are spoiled in a bag of ten? (Hint: spoilage will follow a Poisson distribution, let n=10 and π is the empirical probability.)
0.4 This mean can be used to calculate the Poisson probabilities.
Calculate the mean for the probability distribution shown here. X P(X) 0 0.1 2 0.3 4 0.4 6 0.2
3.4
A binomial distribution has n=10 trials with a probability of success of π=0.4. Calculate the mean of this binomial distribution.
4.0
What shoes the possible outcomes of a random experiment and the probability of each outcome?
A Probability Distribution
Which of the following statements is the best definition of a continuous random variable?
A random variable that can assume any value within a range of values.
The Binomial Probability Formula is P(X)= nCx π ^x(1- π)^n-x. Match the variable from the formula to its description.
C- a combination nCx is the combination of n things taken x at a time. n- number of trials Each experiment consists of n trials. x- random variable The number of successes in n trials. π- P(success) Not the constant 3.1416....
Which of the following statements describe the relationship between the Poisson distribution and the binomial distribution?
It is a limiting form of the binomial distribution when the probability of success (π ) is very small and the sample (n) is very large.
It is easier to use a binomial probability table instead of calculating the probability under what circumstances?
When n is large
Which of the following is not true about binomial probability calculations?
When the x is greater than n, the probability is less than 0. x cannot be greater than n and probability cannot be less than 0.
A random variable can be defined as
a variable observed as the result of an experiment whose value is based on chance.
Suppose that 40% of households use their cell phones for their home phone. If 12 households are randomly selected, what is the probability that at least three use their cell phones? Assume the binomial distribution applies.
0.917
Place the following computational steps in order in which you would do them to find the standard deviation for a probability distribution. Start with the one you would do first at the top.
1. Calculate the mean of the distribution. 2. Subtract the mean from each value and square the difference. 3. Multiply each squared difference by its probability. 4. Sum the products to find the variance.
A binomial distribution has 8 trials and a probability of success of 0.2. Calculate the variance for this distribution.
1.28
Calculate the standard deviation (rounded to one decimal place) of the probability distribution shown here. X P(X) 0 0.1 2 0.3 4 0.4 6 0.2
1.8
Calculate the mean for the probability distribution shown here. X P(X) 10 0.6 20 0.2 30 0.1 40 0.1
17
Suppose a problem asks for the probability of at most four successes when there are only five trials. Which one of these expressions would provide the answer?
P(x=0)P(x=1)P(x=2)P(x=3)P(x=4)
Suppose a problem asks for the probability of more than two successes when there are only ten trials. Which one of these expressions would provide the answer? Select all that apply.
P(x=3)P(x=4).....P(x=9)P(x=10) 1-P(x=0)-P(x=1)-P(x=2) This uses the Complement Rule to find the correct answer.
Which of the following statements describe the Poisson Distribution? Select all that apply
The intervals do not overlap and are independent. The probability of the event is proportional to the interval size. The random variable is the number of occurrences during an interval.
Choose the random variables from this set that are discrete. Select all that apply.
The number of concert tickets sold. The number of people riding on a bus.
Choose the statements that describes characteristics of a probability distribution. Select all that apply.
The probability of an outcome is between 0 and 1. The sum of the probabilities of all possible outcome is one. The outcomes are mutually exclusive events.
Which two of the following statements describe features of a binomial experiment?
The probability of success stays the same for each trial. The random variable counts the number of successes in a fixed number of trials.
A grocer selects five apples randomly from a box, weighs them and calculates an average weight of 165 grams. Match the feature of this process to the correct term.
experiment -> selecting and weighing the apples (the experiment is the activity undertaken)outcome -> 165 grams average weight (a specific result of the experiment)event -> an average weight between 150 and 165 grams (an event is combination of one or more outcomes)random variable -> the average weight of five apples (a numerical rep of an outcome)