Question

In: Statistics and Probability

Mimi plans to make a random guess at 5 true-or-false questions. a. Assume random number X...

Mimi plans to make a random guess at 5 true-or-false questions.

a. Assume random number X is the number of correct answers Mimi gets. As we know, X follows a binomial distribution. What is n (the number of trials), p (probability of success in each trial) and q (probability of failure in each trial)?

b. How many correct answers can she expect to get?

Mimi plans to make a random guess at a test containing 5 true-or-false questions.

a. Mimi plans to make a random guess at 5 true-or-false questions. What is the probability that Mimi will pass the test by random guess?

b. What function can be used to find the probability?

Expert Solution

(a) Number of trials, n = 5

Probability of success in each trial, p = 0.5 (since any one option true or false can be correct both of which has probability of 0.5)

Probability of failure in each trial, q = 1 - p = 0.5

(b) Number of correct answers that she can expect to get = np = 2.5

Here, the criteria of passing the test is not given

(a)

Case 1: When all the answers need to be correct to pass the test, the probability of passing the test by random guess = = 1/32

Case 2: When atleast 4 out of 5 answers need to be correct, the required probability = = 6/32

Case 3: When atleast 3 out of 5 answers need to be correct, the required probability = = 1/2

Case 2: When atleast 2 out of 5 answers need to be correct, the required probability =

= 26/32

(b) Binomial distribution can be used

P(X = x) = , x = 0,1,2,....,n

orchestra answered 1 year ago

true or false if false make the statement right If sales increase by 5% and total...

true or false if false make the statement right If sales increase by 5% and total assets fall by 1%, the TAT ratio would go down by approximately 6% A decrease in the current ratio indicates an improvement in a firm’s liquidity. An increase in the cash coverage ratio means that a firm is less likely to default on its outstanding debt. Ceteris paribus, according to the DuPont framework, an increase in the use of debt would increase a firm’s...

PYTHON Exercise 5. Guess the number 1. Develop a “Guess the number” game. Write a program...

PYTHON Exercise 5. Guess the number 1. Develop a “Guess the number” game. Write a program that comes up with a random number and the player has to guess it. The program output can be like this: I am thinking of a number between 1 and 20. Take a guess. 10 Your guess is too low. Take a guess. 15 Your guess is too low. Take a guess. 17 Your guess is too high. Take a guess. 16 Good job!...

True or False: a.) In a statistical study, the random variable X = 1, if the...

True or False: a.) In a statistical study, the random variable X = 1, if the house is colonial and X = 0 if the house is not colonial, then it can be stated that the random variable is continuous. b.) For a continuous distribution, P(X ≤ 10) is the same as P(X<10). c.) For a continuous distribution, the exact probability of any particular value is always zero. d.) For a binomial probability experiment, with n = 60 and p...

True/ False Questions: For the following questions, first write whether they are true or false then...

True/ False Questions: For the following questions, first write whether they are true or false then write in a few sentences why it’s true or false. (1.5) a. The processes for producing penicillin and blue cheese both use the Penicillium fungus. b. The reproductive organs of Amanita muscaria are popular pizza toppings. c. The fungus Claviceps purpurea is thought to have triggered the infamous Salem witch trials. d. Saccharomyces cerevisiae is a common household bread mold. ...

For students who guess at all answers, find the mean for the random variable X, the number of correct answers?

True or False Questions: Determine if true or false. If false why? 1) Premature efforts to...

True or False Questions: Determine if true or false. If false why? 1) Premature efforts to treat problem behavior before determining its function can be inefficient, ineffective, and even harmful. 2) Research has found that functional analyses conducted in natural environments (e.g., classroom settings) often yield the same (or even clearer) results compared to those conducted in simulated settings. 3) Problem behavior can only be maintained by one function. Behaviors are not multi-functional. 4) Indirect functional assessment procedures are referred...

the following questions are either true or false. 1. Suppose that x is a normally distributed...

the following questions are either true or false. 1. Suppose that x is a normally distributed random variable, with a mean of 10 and a cariance of 4. then probability that x lies between 11.0 and 13.6 is 0.02726 2. Find E(X)= mean id X is a normally distributed random vaeiqvle with standard deviation 1 and if X is a normally distributed random variable with standard deviation 1 and with P(x>5)=0.6915 mean= E(X) =5.50 3. Find P(-0.47<Z<0.94)=0.5666 4. In a...

In Java: Write a program that generates a random number and asks the user to guess...

In Java: Write a program that generates a random number and asks the user to guess the number and keeps track of how many guesses it took If the user input is negative or zero then the loop must stop reading further inputs and display how many guesses they used If they guess the correct number display a message telling them they got it and exit the program If they guess the wrong number (but still a legal guess) you...

Let X be a random variable that is equal to the number of times a 5...

Let X be a random variable that is equal to the number of times a 5 is rolled in three rolls of a fair 5-sided die with the integers 1 through 5 on the sides. What is E[X2 ]? What is E2 [X], that is, (E[X])2 ? Justify your answers briefly

Please indicate if the statement below is true or false. If the statement is false, indicate and make the correction to make the statement true.

Modified True/FalsePlease indicate if the statement below is true or false. If the statement is false, indicate and make the correction to make the statement true. Each question is worth 5 points (there is a bonus). Partial answer (that is, the statement is false, but your correction is wrong) will get ½ credit.1. General obligation bonds are less restrictive than revenue backed bonds with few limitations regarding the amount that can be issued.True/False ____________________ Correction to make true ___________________________________________________________________________________2. When issuing revenue backed bonds, receipts from all...