Stat 200 quiz 5

C Feedback: if a random variable is continuous it cannot also be discrete

A random variable cannot be both continuous and A) skewed. B) uniform. C) discrete. D) normal.

A Feedback: Keep in mind that a gallon is a measurement and that if you buy a gallon of OJ you probably do not get exactly one gallon.

Correcly identify if the following random variables as either discrete or continous. A gallon of orange juice. A) Continuous B) Discrete

B Feedback: Not binomial - what is a few?

Correctly identify whether the following situations satisfy the conditions required to conduct a Binomial experiment. Selecting a few voters from a very large population of voters and observing whether or not each of them favors a certain proposition in an election when 54% of all voters are known to be in favor of this proposition. A) Binomial B) NOT Binomial

A Feedback: Time is continuous. Imagine if an email is said to have lost 10 pounds. This 10 pounds is actually pounds from 9.5 seconds to less than 10.5

For the given situation, decide if the random variable described is a discrete random variable or a continuous random variable. Random variable X = the weight (in pounds) a dieter will lose after following a two week weight loss program. A) Continuous random variable B) Discrete random variable

A Feedback: At least 4 students means 4 or more. In this scenario this would mean only 4 since there were only 4 students in the sample. The P(X=4) is 0.0016

From the table above, what is the probability that at least four college students in this sample abstain from drinking? A) 0.0016 B) 1.00 C) 0.9984

A Feedback: The standard deviation is simply the square root of the variance: square root of 1.16 is 1.08. Note that when reporting standard deviation we always use the positive square root.

Joan has noticed that the probability distribution for X = number of students in line to use the campus ATM machine when she shows up to use it is shown above. The variance of X, V(X) = 1.16. What is the standard deviation of X? A) 1.08 B) 1.16 C) 1.35 D) 2.20

D Feedback: You are asked to find P(X < 85) which you have to convert to P(Z < 1.5) by using z-score = (observed - mean)/SD. From the Standard Normal Table look up 1.5 in the left column combine with 0.00 across the top row, we get 0.9332

Scores on an achievement test had an average of 70 and a standard deviation of 10. Serena's score was 85. Using Standard Normal Table and assuming the scores have approximately a normal distribution, about what proportion of students scored lower than Serena? A) 0.68 B) 0.84 C) 0.07 D) 0.93

A Feedback: Expected values are the mean results expected over a long run (i.e. large number) of trials.

Suppose that for X = net amount won or lost in a lottery game, the expected value is E(X) = -$0.50. What is the correct interpretation of this value? A) Over a large number of plays the average outcome for plays is a net loss of 50 cents. B) The most likely outcome of a single play is a net loss of 50 cents. C) A player will have a net loss of 50 cents every single time he or she plays this lottery game. D) A mistake must have been made because it's impossible for an expected value to be negative

A Feedback: You are asked to find P(X > 60) which you have to convert to P(Z > 0.0) by using z-score = (observed - mean)/SD. From Table A1 and using the complement rule, look up 0.0 in the left column combine with 0.00 across the top row, we get 0.5000. Subtracting this value from one produces P(Z > 0.0) = 0.5000

The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. Using Standard Normal Table, what is the probability that a randomly chosen student will take at least an hour to complete the exam? A) 0.5000 B) 0.8413 C) 0.9772 D) 0.1587

A Feedback: The expected value is what result is the mean value you would expect to find in a long run observation of the variable

The expected value of a random variable is the A) mean value over an infinite number of observations of the variable. B) largest value that will ever occur. C) value that has the highest probability of occurring. D) most common value over an infinite number of observations of the variable.

C Feedback: The z-score is found by (observed - mean)/SD = (20 - 30)/5 = - 2.0

The time taken for a computer to boot up, X, follows a normal distribution with mean 30 seconds and standard deviation 5 seconds. What is the standardized score (z-score) for a boot-up time of x =20 seconds? A) 2.0 B) 0.0 C) -2.0 D) 1.0

C Feedback: Find the probability of less than -2.56 (= 0.0052) and the probability of greater than 1.51 (1 - 0.9345 = 0.0655) and add these two together to get 0.0707

Using Standard Normal Table, find the probability that a z-score is less than -2.56 or greater than 1.51. A) 0.9397 B) 0.9537 C) 0.0707 D) 0.0847

B Feedback: This is looking for greater than meaning you have to subtract from 1 the probability found in the table for 0.5. This comes to 1 - 0.6915 = 0.3085

Using Standard Normal Table, the probability of an observation being greater than 0.5 is A) 0.6915 B) 0.3085

B Feedback: From Table A1 we need to apply P(Z < 1.45) - P(Z < -1.2). From the table, look up 1.4 in the left column combine with 0.05 across the top row, we get 0.9265, and look up -1.2 in the left column combine with 0.00 across the top row, we get 0.1151. Subtracting 0.9265 - 0.1151 equals 0.8114

Using Standard Normal Table, what is the probability that Z is between -1.2 and 1.45, P(-1.2 < Z < 1.45)? A) 0.8041 B) 0.8114 C) 0.0303 D) 0.7740

B Feedback: From Table A1 and using the complement rule, look up 2.0 in the left column combine with 0.00 across the top row, we get 0.9772. Subtracting this value from one produces P(Z > 2) = 0.0228

Using Standard Normal Table, what is the probability that Z is greater than 2, P(Z > 2)? A) 0.9772 B) 0.0228 C) 0.2000 D) 0.5000

D Feedback: You need to use algebra to solve for "observed" in the equation z-score = (observed - mean)/SD. Generally, this works out to observed = SD*z-score + mean. Substituting, observed = (100)*(1.65) + 500 which equals 665

Verbal SAT scores have approximately a normal distribution with mean equal to 500 and standard deviation equal to 100. The 95th percentile of z-scores is z = 1.65. What is the 95th percentile of verbal SAT scores? A) 335 B) 500 C) 600 D) 665

B Feedback: Needing a fixed number of trials with a "success" or "failure" on any one trial, and a fixed, common probability for each success leads to the correct answer of randomly guessing on a 15 question true/false test

Which of the following is an example of a binomial random variable? A) The number of games your favorite baseball team will win this coming season. B) The number of questions you would get correct on a 15 question true-false test if you randomly guessed on all questions. C) The number of coins a randomly selected student is carrying. D) The number of siblings a randomly selected student has.

C Feedback: Cumulative probability implies "from the beginning to some point", or in other words the probability from some value or less.

Which one of the following probability statements would represent a cumulative probability? A) The probability that there are exactly 4 people with Type O+ blood in a sample of 10 people. B) The probability that the accumulated annual rainfall in a certain city next year, rounded to the nearest inch, will be 18 inches. C) The probability that a randomly selected woman's height is 67 inches or less. D) The probability of exactly 3 heads in 6 flips of a coin.

D Feedback: Since we need a fixed n this rule out all answers except "Number of women taller than 68 inches in a random sample of 5 women". For this response n is fixed at 5

Which one of these variables is a binomial random variable? A) Number of textbooks a randomly selected student bought this term. B) Number of CDs a randomly selected person owns. C) Time it takes a randomly selected student to complete a multiple choice exam. D) Number of women taller than 68 inches in a random sample of 5 women.

C Feedback: Time is continous as it is &$8220;measured".

Which one of these variables is a continuous random variable? A) The number of correct guesses on a multiple choice test. B) The number of women taller than 68 inches in a random sample of 5 women. C) The time it takes a randomly selected student to complete an exam. D) The number of tattoos a randomly selected person has.