QUESTION: 80% of the Quant 2600 students pass the class. Assume that ten students are registered for the course.
a. What probability distribution works best for this problem? Binomial, Poisson, Hypergeometric, or Normal
b. What is the expected number of students that will pass the
course? (2 decimal places) c. What is the standard deviation of
students that will pass the course? (2 decimal places) d. What is
the probability that exactly 8 will pass the course? (4 decimal
places)
e. What is the probability that at least 8 students will pass the
course? (4 decimal places)
In: Statistics and Probability
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and 1 coin that lands heads with probability 1/4 . A coin is taken from the box at random and flipped repeatedly until it has landed heads three times. Let X be the number of times that the coin is flipped and Y be the probability that the coin lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of Y .
(b) Compute E(X).
(c) Compute var(X).
In: Statistics and Probability
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and 1 coin that lands heads with probability 1/4 . A coin is taken from the box at random and flipped repeatedly until it has landed heads three times. Let X be the number of times that the coin is flipped and Y be the probability that the coin lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of Y .
(b) Compute E(X).
(c) Compute var(X).
In: Statistics and Probability
15. a. (1pt) The probability of rolling a 6 (a normal numbered cube) is ______________
15. b. (2pts) Assume that you are going to do 10 rolls of this numbered cubes and you are focused on the number of times the side with the six comes up. What is the probability of having exactly 8 sixes appear?
15. c. (2 pts) What is the mean and the standard
deviation?
15 d. (3pts) Using the words mean and standard deviation, explain
(using your own words) why the probability in 15b is so small.
In: Statistics and Probability
According to a study, 50 % of adult smokers started smoking before 21 years old. 14 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.
1. The probability that at least 4 of them started smoking before
21 years of age is?
2. The probability that at most 8 of them started smoking before 21
years of age is?
3. The probability that exactly 2 of them started smoking before 21
years of age is ?
In: Statistics and Probability
In a poll conducted by the General Social Survey, 79% of respondents said that their jobs were sometimes or always stressful. Two hundred workers are chosen at random. Use the TI-84 Plus calculator as needed. Round your answer to at least four decimal places.
(a) Approximate the probability that 165 or fewer workers find their jobs stressful.
(b) Approximate the probability that more than 158 workers find their jobs stressful.
(c) Approximate the probability that the number of workers who find their jobs stressful is between 152 and 177 inclusive.
In: Statistics and Probability
Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 124 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. Round your answers to two decimal places (e.g. 98.76). (a) What is the probability that every passenger who shows up gets a seat? (b) What is the probability that the flight departs with empty seats? (c) What are the mean and (d) standard deviation of the number of passengers who show up?
In: Statistics and Probability
Data collected over a long period of time showed that 1 in 1000 high school students like mathematics. A random sample of 30,000 high school students was surveyed. Let X be the number of students in the sample who like mathematics
a) What is the probability distribution of X?
b) What distribution can be used to approximate the distribution of X? Explain.
c) Find the approximate probability of observing a value of X equal to 40 or more?
d) Find the approximate probability of observing a value of X between 35 and 40 inclusive ?
In: Statistics and Probability
Data collected over a long period of time showed that 1 in 1000 high school students like mathematics. A random sample of 30,000 high school students was surveyed. Let X be the number of students in the sample who like mathematics
a) What is the probability distribution of X?
b) What distribution can be used to approximate the distribution of X? Explain.
c) Find the approximate probability of observing a value of X equal to 40 or more?
d) Find the approximate probability of observing a value of X between 35 and 40 inclusive ?
In: Statistics and Probability
Concrete blocks are produced in lots of 2000. Each block has probability 0.85 of meeting a strength specification. The blocks are independent.
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
1-What is the probability that, in a given lot, fewer than 1690 blocks meet the specification?
2-Find the 70th percentile of the number of blocks that meet the specification.
3-In a group of six lots, what is the probability that fewer than 1690 blocks meet the specification in three or more of them?
In: Statistics and Probability