4b
The table 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
Suppose that 25% of adults exercise regularly. If 11 adults randomly selected, what is the probability that four or less exercise regularly? Assume the binomial distribution applies.
0.885
3 4.5 0.87 0.33
Range Mean standard Deviation P(X)
Which of the following is the best description of the shape of a uniform distribution?
Rectangular
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
A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 400 and 500?
0.2139
A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 600 and 700?
0.2706
Which of the following statements are true of the Standard Normal Distribution?
The standard deviation (σ) is 1 The mean (μ) is zero.
Approximately 68% Approximately 95% Approximately 99.7%
μ ± σ μ ± 2σ μ ± 3σ
A uniform distribution has a minimum value for the random variable of "a" and a maximum of "b". What is the formula for the standard deviation of the distribution?
σ=(b−a)212⎯⎯⎯⎯⎯⎯⎯⎯⎯√
The Dean's secretary receives an average of 3 calls per hour. Assuming the Poisson distribution applies, what is the probability that th secretary will receive 6 calls next hour?
0.050
Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 490 and 560?
0.2823
Applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen applicant will score between 550 and 650?
0.3851
A grocer 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
Applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen applicant will score between 500 and 600?
0.4186
A cellular communications company finds that on average it drops about 300 calls for every 1000 calls placed. What is the mean number of dropped calls for ten calls placed? (Hint: dropped calls follow a Poisson distribution. Let n=10 and π is the empirical probability.)
3
A binomial distribution has n = 12 trials with a probability of success of π=0.3. Calculate the mean of this binomial distribution.
3.60
A binomial distribution has n = 10 trials with a probability of success of π=0.4. Calculate the mean of this binomial distribution,.
4
Suppose the grades on a particular test are uniformly distributed between 60 and 96. What is the mean of this distribution?
78.0
What percentage of the area under the normal curve is more than 1 standard deviation from the mean?
Approximately 16%
Which of the following statements is true for both the binomial and Poisson distributions?
Both are discrete probability distributions.
Which of the following is true regarding continuous and discrete random variables.
Continuous random variables usually result from measuring.
What do we mean when we say there is a "family" of normal distributions? Choose two of these statements.
Distributions may have different means and standard deviations but still be "normal" in shape. A single equation describes all normal distributions
How would you describe the shape of the Normal Distribution?
It is "bell" shaped, and symmetrical with the center at μ.
Which of the following statements describes 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.
Which statements describe the mean of a Uniform Distribution. Select all that apply.
It is always equal to the median. It is always in the middle of the minimum and maximum values.
Where does the curve of the normal distribution touch the x-axis?
It never touches, but approaches asymptotically in both directions
The area under a uniform distribution (or any probability distribution) represents a probability. Which one of the following statements characterizes this area?
The total area is one.
The minimum and maximum values of the random variable are sufficient to describe which of these distributions?
Uniform
It is easier to use a binomial probability table instead of calculating the probability under what circumstances?
When n is large.
Z X μ σ
a standard normal random variable a normal random variable the mean of x the standard deviation of X
For a uniform distribution, the probability is defined as P(x) = 1b−a1b-a. What do the symbols b and a represent?
the minimum and maximum values
The average weight of a Honeycrisp apple is 110 grams and the standard deviation is 20 grams. What is the z-value for an apple that weighs 140 grams?
z = 1.5
The average score on an IQ test is 110 and the standard deviation is 10. What is the z-value for a score of 130?
z = 2
Which of the following formulas is used to convert a normally distributed random variable, X, to a z-value?
z = X−μσ
A Uniform distribution has a minimum value for the random variable of "a" and a maximum of "b". What is the formula for the mean?
μ = a+b2
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
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
The time it takes a wholesaler to fill an order follows a uniform distribution from three to six days What is the probability that they will fill an order between day 3 and 5?
2/3
A binomial distribution has 8 trials and a probability of success of 0.2. Calculate the variance for this distribution.
1.28
The duration of a red light at a particular intersection in a city is uniformly distribution from one to four minutes. What is the probability that you will wait at the particular red light between 2.5 and 3 minutes?
1/6
Suppose that customer usage time of computers in the public library is uniformly distributed with a minimum of 20 minutes and a maximum of 80 minutes. What is the standard deviation of the distribution?
17.3
A binomial distribution has 12 trials and a probability of success of 0.4. Calculate the variance for this distribution.
2.88
What are the upper and lower limits of the random variable for the Normal distribution?
No limits. It is asymptotic in both directions.
A Uniform Distribution has the same probability for any x such that a≤x≤b. What is this probability?
P(x) = 1b−a
Which of the following statements are true about the symmetric characteristic of the normal probability distribution? Select all that apply.
The shape to the left of the mean is a mirror image of the shape to the right of the mean. The area on each side of the mean equals one-half.
Which of the following is an example of a continuous random variable?
The square footage of a house.
Which statements below accurately characterize a uniform distribution. Select all that apply.
The area inside the rectangle (i.e the frequency polygon) must be one. Areas within the distribution represent probabilities.
Since the normal probability distribution is symmetrical about the mean, which of the following is true?
The area on each side of the mean is 0.5.
Which of the following statements are true with respect to both the Standard Normal distribution and any normal probability distribution? Choose all that apply.
The areas are equal to 1. A normal probability distribution can be converted into a standard normal distribution.
Which is the best definition of the z-value?
The distance between a value x and the mean, μ, divided by the standard deviation, σ
Suppose you have two normal distributions: one has μ = 16 and σ = 2 and the other has μ = 20 and σ = 3. Which of the following statements are true? Select all that apply.
The distribution with σ = 2 is more peaked. The distribution with μ = 20 is to the right of the other distribution.
Continuous random variables usually result from measuring.
The intervals overlap and are not independent.
Which of the following statements are not true of the Poisson Distribution?
The intervals overlap and are not independent.
What determines the width and location of the Normal Distribution?
The mean (μ) determines the location and the standard deviation (σ) determines the width.
Which one of the following is a result of the normal probability distribution being bell-shaped?
The mean, median, and mode are at the center.
μ e x P(x)
The mean; μ = nπ 2.71828... number of occurrences probability of a specific x
Which one of the following is true about the uniform distribution?
The minimum is identified as 'a' and the maximum is identified as 'b'.
Which of the following statements describe the Poisson Distribution? Select all that apply
The probability of the event is proportional to the interval size. The random variable is the number of occurrences during an interval. The intervals do not overlap and are independent.
A z value is a distance from the (blank), , measured in units of the standard deviation.
mean