statistics ch6 exam pdf
In a certain video game you wish to be in the top 0.15% of the scores. Assuming that the scores are normally distributed with a mean score of 25,460 and a standard deviation of 570, what is the score you need to achieve?
27,170
If the standard deviation is 5, the mean is 40, and the value in question is 45, then what is the Zscore?
1
If the standard deviation is 10, the mean is 50, and the value in question is 30, then what is the Z-score?
-2
Mathew is a math teacher who has recently conducted an exam in his class. The mean score result is 62, while the standard deviation was 20. Assume that the scores are normally distributed. If a student scored 42 points, what was his z score?
-1
If z = 2 and -2, what area falls OUTSIDE these z values on a standard normal curve?
0.046
The lifespan of a certain battery is measured in cycles. A manufacturer claims that the average number of cycles for their battery is 2000 with a standard deviation of 100, and the number of cycles is distributed normally. You wish to buy a battery from this manufacturer. What is the probability that the battery will last between 1900 and 2200 cycles?
0.815
A store sells suits that are only designed for men who are very tall. The smallest suit they make fits any man who is 75 inches tall. If the average height of men is 70 inches, with a standard deviation of 5 inches, then how many men can shop at this store? Use this z score table:
15.87%
You are creating a tree house and have made the doorway into the structure 71 inches tall. Suppose the average height of adult males is 68 inches with a standard deviation of 3 inches. What percentage of men will have to bend their heads to get into the house?
16%
You have a fair coin and want to calculate the probability that if you flip the coin 20 times, you will get at least 14 heads. What is the probability that you will get heads MORE than 14 times?
2%
The tail lengths of a certain animal are normally distributed with a mean length of 1.5 feet and a standard deviation of 3 inches. What percentage of these animals have a tail that is at most one foot long?
2.5%
The police have noted that they, on average, only need 2 police cars to patrol a 50-square-mile area in order to uphold the law, with a standard deviation of 1.25. Assume that the distribution is normal. What is the percentage chance that the police will require more than 3 police cars to monitor the area?
21%
A statistician is studying a normally distributed population, and they are interested in the data that falls from the mean to one standard deviation above the mean. What percentage of the population falls within this range?
34%
James is a teacher in a small school is Boston. He is amused to find that his data is normally distributed, with 30 of his students taking a test which has 70 points. The average of their test scores is 36 and the standard deviation is 7. If the distribution is normal, towards which value is this symmetric data centered?
36
On a history exam, the average score was 75, with a standard deviation of 15. Assume that the distribution of the scores is normal. What percentage of the class scored between 60 and 80 points?
47%
Tamara is a math teacher in high school. She has noticed that her recent exam results have a normal distribution. What portion of the exam results will NOT be included within two standard deviations of the mean?
5%
In a college class, the average IQ is 115. Assume that the distribution is normal and that the standard deviation is 15. What percentage of the class has an IQ between 105 and 130? (Use a Z table, not provided. Please use the link in the chapter description or do a search.)
59%
In a college class, the average IQ is 115. Assume that the distribution is normal and that the standard deviation is 15. What percentage of the class has an IQ between 105 and 130?(Use a Z table, not provided. Please use the link in the chapter description or do a search.)
59%
What is the area between z-scores of -1 and 1?
68%
_____ of normally distributed data is always contained within 1 standard deviation of the mean.
68%
Russell is a history teacher who recently held an exam in his class. The mean score result is 65, while the standard deviation was 20. Assume that the scores are normally distributed. If a student's z-score was 1.5, how many points did he score on the exam?
95
What is the area between z-scores of -2 and 2?
95%
_____ of normally distributed data is always contained within 2 standard deviations of the mean.
95%
What is the area between z-scores of -3 and 3?
99.7%
_____ of normally distributed data is always contained within 3 standard deviations of the mean.
99.7%
Which of the following scenarios exemplifies a process that would be described by a continuous random variable?
A group of statistics students measures the height distribution of the population of Seattle, Washington.
What is standard deviation?
A measure of how scattered a data set is.
What is a Z-score?
A measurement of the distance from the mean to a point in terms of standard deviations
What is a frequency distribution that can be represented by a bell-shaped curve?
A normal distribution
How do we know that a continuous probability function doesn't contain holes, jumps, or vertical asymptotes?
Because it's a continuous function.
Why is a measurement of weight distribution among a population an example of continuous probability distribution?
Because there are potentially infinitely many possible measurements of weight, so there is an uncountable number of possible outcomes.
Why would height be defined by a continuous random variable?
Because there is an infinite spectrum of possible heights
Why is rolling dice an example of a process associated with discrete probability distribution?
Because when one rolls dice, there is a countable number of possible outcomes.
Why is the result of rolling a die considered a discrete random variable?
Because when you roll a die, there is a countable number of possible outcomes.
Which of the following must be true to be able to approximate binomial probabilities with a normal distribution?
Both np>=5 and nq>=5
How might a person apply the continuous probability distribution to a real-life situation?
By repeatedly measuring the amount of time it takes them to swim one lap in a pool, then figuring out the probability that they will complete a lap in a particular amount of time.
Which type of probability distribution is used when there is an uncountable number of possible outcomes? Continuous prob
Continuous probability distribution
A person is rolling a die, and records the outcome of each roll. Which type of random variable captures this situation? Why?
Discrete, because there are only a finite number of possible outcomes.
Which of the following situations is best modeled by a discrete random variable?
Drawing cards from a deck, and calculating the probability of drawing a certain hand.
Which of these would have the largest area?
Everything under a Z-score of 2
Which of the following is a property that any continuous probability density function f(x) must satisfy? For any x, f(x) is always less than one half.
For any x, f(x) is always greater than or equal to zero.
A student wants to compute the expected value of a continuous probability distribution describing the heights of a population of bears. Which of the following would she use?
Integration
Solving for the expected value of a continuous probability distribution involves which of the following?
Integration
Which of the following is TRUE regarding the expected value associated with the probability density function?
It can be thought of as the long term-average value of the probability distribution.
Which of the following is TRUE about the expected value?
It is a measure of the center of the probability distribution
Why is flipping a coin an example of a discrete random variable?
It is associated with a countable number of outcomes.
Which of the following is FALSE regarding the binomial probability distribution?
It is calculated based on a formula where p is the significance level for a single event and q is the quantity of data present.
Which of the following is FALSE regarding the binomial probability distribution? a
It is calculated based on a formula where p is the significance level for a single event and q is the quantity of data present.
A distribution of data has a mean of 15 and a standard deviation of 2. How many standard deviations away from the mean is a value of 13?
It is one standard deviation below the mean
A statistician consults a continuous probability distribution, and is curious about the probability of obtaining a particular outcome a. Which of the following is definitely true of the value of P(X=a)?
It's zero
Which of the following is an example of a process that would be described by a continuous random variable?
Measuring the height distribution of a population
A continuous probability distribution function is also known as which of the following?
Probability density function
What do we call a graph of probabilities associated with all the possible values taken by a continuous random variable?
Probability density function
Assuming that both np>=5 and nq>=5, how can you calculate the standard deviation of the normal distribution?
Standard deviation = sqrt(npq)
To compute the expected value of a discrete probability distribution, which of the following is used?
Summation
What do one-sided problems involve?
The area to the left or to the right of a single Z-score
What do two-sided problems involve?
The area within or outside of a range defined by two Z-scores.
In a probability distribution function, what does the x-axis typically represent?
The possible values the random variable can take
If we measure a finite area under the curve of the probability density function when a and b fall in a domain of the function where a and b have positive nonzero values in the interval (a, b), when a < b, then which of the following is TRUE?
The probability of an outcome within the interval (a, b) is not equal to zero
In a probability distribution function, what does the y-axis typically represent?
The probability of each outcome
Which of the following is TRUE about continuous random variables?
They involve processes where the total number of possible outcomes is uncountable.
A statistician has figured out the percentage of the area under a normal curve that meets certain criteria. How would they apply this knowledge to a given sample?
They would multiply the percentage by the total sample size.
Which of the following is associated with a continuous random variable?
Weight measurements within a population
Identify which of the following distributions has the largest spread:
When the mean is 11 and the standard deviation is 4.
If you're using the binomial probability formula to capture the probability of an event, and you know the value of q, will you always be able to calculate the value of p? Why?
Yes, because the only possible outcomes are success (p) and failure (q), so p + q = 1.
Which has the lowest area under it?
Z-score of -3
A teacher is satisfied with his test results as they seem to reflect a normal, or Gaussian, distribution. This means that the data has a _____ probability distribution.
continuous
Which of the following is an example of a process that would be described by a discrete random variable?
flipping a coin
For which of the following random processes would you define a discrete random variable?
flipping coin
Solving for the expected value of a continuous probability distribution involves _____.
integration
Negative Z-scores appear on the _____ side of the normal distribution
left
Where is the normal distribution curve at its highest point?
mean
Assuming that both np>=5 and nq>=5, how can you calculate the mean of the normal distribution?
mean= np
In a normal distribution, 68% of the data is within _____ standard deviation of the mean.
one
Which side of the normal distribution does the positive Z-score appear on?
right
What is the fastest way to find Z-score percentages?
tables
Six Sigma seeks to limit errors to occur only outside of _____ standard deviations.
three
The _____ is a measure of distance from the mean in terms of how many standard deviations it is removed from the mean
z-score
Mark conducted a math test and the mean result of his students was 73, with a variance of 49 (standard deviation = 7). The grade excellent was achieved by all students who scored 86 points or higher. Assume that the grades are normally distributed and the class has 100 students. How many students managed to get an excellent grade?
3
mark conducted a math test and the mean result of his students was 73, with a variance of 49 (standard deviation = 7). The grade excellent was achieved by all students who scored 86 points or higher. Assume that the grades are normally distributed and the class has 100 students. How many students managed to get an excellent grade?
3
You have a fair coin and want to calculate the probability that if you flip the coin 20 times, you will get EXACTLY 14 heads. What is the probability for this event?
3.7%
On a history exam, the average score was 65, with a standard deviation of 10. Assume that the distribution is normal. What percentage of the class managed to have a score higher than 70 points? (You need to use a Z table, either the one linked to in the chapter description or you can search for one.)
31%
