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rd deviation of 3.2 hours. A sample of 35 high school seniors is selected. Find the following values, if possible. Please round your answers to four decimal places. If you should not find a probability, please write NA for your answer.
What is the probability that the sample mean studying time is between 4 and 5 hours?
What is the probability that the sample mean studying time is less than 6 hours?
What is the probability that the sample mean studying time is more than 8.5 hours?

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When selecting one card from a standard deck, what is the probability of selecting a Jack AND a Club?
An urn contains 10 red balls, 6 green balls, 15 orange balls, and 14 blue balls.
If one ball is randomly drawn from the urn, what are the odds against the ball being green?
The odds against an event are 7 to 1. Find the probability that the event will occur?
The probability of an event is 7/10. Find the odds against that event.

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of Sport-Equip Ltd, a company that sells sports equipment. Some of the users
who visit the website end up buying sports equipment from the website while others are
simply browsing in order to obtain product information.
(a) Clearly explain and justify which probability distribution you would use to
describe the number of Internet users who visit the website of Sport-Equip Ltd
in a one hour period. [There is no need to calculate any probabilities for this part
of the question]
(5 marks)
(b) What is the probability that during any half-hour period, there will be less than 3
visitors to the website?
(5 marks)
(c) What is the probability that during any two-hour period, there will be more than
15 visitors to the website?
(5 marks)
(d) If a user has just visited the website, find the probability that the website will
have another visitor within the next 10 minutes. In your answer, state the
probability distribution you have used and explain your choice.
(4 marks)
(e) It is estimated that 40% of Internet users who visit Sport-Equip Ltd’s website
buy a product from the company. If 100 users visit the website over a given
period of time, find the probability that more than 50 of them will buy a product
from the company. In your answer, state the probability distribution you have
used and explain your choice

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4.In a box there are 4 red, 4 blue and 3 white marbles. Two marbles are selected at random and ...

or is noted. Find the probability that neither is white given that neither is red.Round your answer to 4 decimal places
A place kicker in the NFLmakes 78% of his field goals. If the outcomes are independent, what is the probability that he makes exactly 6 of the next 8 field goals? Round your answer to 4 decimal places
There are 5 white mice and 3 gray mice in a cage. Three mice are selected at random and their colors are noted. Find the expected number of white mice.Round your answer to 2 decimal places

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ty distribution:
x 3 5 8 10
pX(x) k k k 2k
i. Determine the constant k and hence write down the probability
distribution of X.
ii. Find E(X), the expected value of X.
iii. Find Var(X), the variance of X.

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y aces or twos, you lose the game immediately. You also lose if you draw picture cards(J,Q,K) more than twice. In this question, you’ll study the probability of winning this game.(a) What is the probability of drawing no aces or twos after thirteen draws?(b) Given you have drawn thirteen times, none of which is aces or twos, what is the probability that you draw at most two picture cards?(c) What is the probability to win this game?
12. Suppose you are tossing an unbiased coin for100times.(a) What is the probability of getting50heads and50tails?(b) LetXbe the random variable counting the number of heads you observe in this exper-iment. What is the expected value ofX? What is the variance ofX? What is thestandard deviation ofX?
13. The following are probability distributions for two random variablesX,Y.
kPr(X=k)
0,0.4
1,0.3
2,0.3
kPr(Y=k)
0,0.5
1,0.3
2,0.2
(a) Construct the probability distribution table for the random variableXY.(b) Find E[X],E[Y] and E[XY]. Is is true that E[XY] =E[X]E[Y]?(c) Find the variances σ2X,σ2Y,σ2XY of X,Y and XY. Is it true that σ2XY=σ2Xσ2Y?
14. The aliens who are fond of gambling came back to play another game with you. In this game, you first toss a coin5times. If you observe3or fewer tails, you roll a die3times. If youobserve4or more tails, you roll a die20times. What is the probability that you end up with at most two6’s in your dice rolls?
15. (Challenge question, worth2points) You have two bags, each of which contains10marbles.Each time you remove a marble from a random bag. What is the probability that after one of the bags is emptied, there are still exactly3marbles in the other bag?

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7.There are 4 sets of balls numbered 1 through 12 placed in a bowl. If 4 balls are randomly chosen ...

hout replacement, find the probability that the balls have the same number. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

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- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to find the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

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- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to find the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

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- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to find the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

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6 minutes and the variance of the waiting time is 9. Find the probability that a person will wait for between 1 and 9 minutes. Round your answer to four decimal places.

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on with mean 81 and standard deviation 22. I have been asked to find the probability that X (bar) is greater than 86 and to find the 85th percentile of this data set

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ose
the breaking point is uniformly distributed on the chalk. Let X denote the length of the shorter piece and
R the ratio of the lengths of the shorter to the longer piece. Then X has uniform distribution on [0; 1
2 ].
(a) (6pts) Find the probability density function of R.
(b) (8pts) Find the mean and variance of R.

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consumes each year is 196 with a standard deviation of
22 pounds (Source: American Dietetic Association). If a sample of 50 individuals is randomly selected, find
the probability that the mean of the sample will be less than 200 pounds.

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15. 6 male 2 female 2 people age range 18-21 5 people age range 22-25 1 person age range 26-30 7 of them ...

of them study international business
1 hospitality
2 Ethiopian 2portuguese
1 Ukrainian
1 kazakhistani
1 zimbabwean
8 of them use social media
1 person mostly use Facebook
1 person use YouTube
6 people instagram
2 people have more than 3 accounts
3 people have 3 accounts
2 people have 2 accounts
I have to find Mean,Median,Mode, Standard deviation and Probability distribution

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f them study international business
1 hospitality
2 Ethiopian 2portuguese
1 Ukrainian
1 kazakhistani
1 zimbabwean
8 of them use social media
1 person mostly use Facebook
1 person use YouTube
6 people instagram
2 people have more than 3 accounts
3 people have 3 accounts
2 people have 2 accounts
I have to find Mean,Median,Mode, Standard deviation and Probability distribution

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ppose a package of M&M’s typically contains 52
M&M’s.
a.) State the random variable.
b.) Argue that this is a binomial experiment
Find the probability that
c.) Six M&M’s are brown.
d.) Twenty-five M&M’s are brown.
e.) All of the M&M’s are brown.
f.) Would it be unusual for a package to have only brown M&M’s? If this were
to happen, what would you think is the reason?

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weighing between 140 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 145 lb and a standard deviation of 29.9 lb.
a. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 191 lb.

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is a multiple of three or greater than eight.
A certain game consist of rolling a single fair die and pays off as follows nine dollars for a six, six dollars for a five, one dollar for four and no payoffs otherwise.Find the expected winnings for this game.
A fair die is rolled four times. A 6 is considered success While all other outcomes are failures find the probability of three successes.
A pet store has nine puppies including 4 poodles 3 terriers and 2 retrievers. If Rebecca an errand in that order each select one puppy at random without replacement find the probability that Aaron select a retriever given that from last Rebecca selects a poodle.
Experience shows that a ski lodge will be for (166 guests) if there is a heavy snowfall in December, well only partially full (52 guests) With a light snowfall. What is the expected number of guests if the probability for a heavy snowfall is 0.40? I assume that heavy snowfall and light snowfall are the only two possibilities.
A pet store has six puppies Including two poodles two Terriers and to retrievers. If Rebecca and Aaron in that order each select one puppy random with replacement (They both may select the same one) Find the probability That Rebecca selects a terrier and Aaron selects a retriever.
Three married couples arrange themselves randomly in six consecutive seats in a row. Determine (A) the number of ways the following event can occur, And (B) the probability of the event. (The denominator of the probability fraction will be 6!=720, The total number of ways to arrange six items ). Each man was that immediately to the right of his wife.
A coin is tossed five times. Find the probability that all our heads. Find the probability that at least three are heads.
A certain prescription drug is known to produce undesirable facts and 35% of all patients due to drug. Among a random sample of a patient using a drug find the probability of the stated event. Exactly 5 have undesired effects.
10,000 raffle tickets are sold. One first prize of 1600, for second prizes of 800 each, And 9/3 prizes of 300 each or to be awarded with all winners selected randomly. If you purchase one ticket what are your expected winnings.
Suppose a charitable organization decides to Raise money by raffling A trip worth 500. If 3000 tickets are sold at one dollar each find the expected net winnings for a person who buys one ticket. Round to the nearest cent
Three men and seven women are waiting to be interviewed for jobs. If they are selected in random order find the probability that all men will be interviewed first
A fair diet is rolled. What is the probability of rolling on our number or a number less than three.
The pet store has 15 puppies, including five poodles, five Terriers, and five retrievers. If Rebecca and Aaron, in that order, select one puppy at random without replacement, find the probability that both select a poodle
Beth is taking a nine question multiple-choice test for which each question Has three answer choices, only one of which is correct. Beth decides on answering By rolling a fair die And making the first answer choice if the die shows one or two, The second If the die shows three or four, and the third if the die shows five or six. Find the probability of the stated event. Exactly 6 correct answers
For the experiment of drawing a single card from a standard 52 card deck find (a) the probability and (b) the odds are in favor that they do not drive six

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with a mean of 25 gm and a standard deviation of 5 gm.
(a) If the machine is used 500 times, approximately how many times will it be expected to dispense 30 gm or more of chilli sauce?
(b) How can you decrease this number to half? Give a numerical answer.
2. StarTech manufactures re sensors. They use a protective screen for their sensors to protect it from dust. The sensor becomes useless if the thickness of the screen exceeds 0.5 mm. They outsource the production of the screen to a di erent company that claims to manufacture screens with a mean thickness of 0.3 mm and a standard deviation of 0.1 mm.
(a) If 10000 screens are manufactured how many will be discarded because they are too thick?
(b) If screens less than 0.2 mm are too thin to be used, what is the probability that screens manufactured by the above company will be discarded because they are too thick or too thin? Show the result on a graph.
3. The amount of time that Sam spends playing the guitar is normally distributed with a mean of 15 hours and a standard deviation of 3 hours.
(a) Find the probability that he spends between 15 and 18 hours playing the guitar during a given week.
(b) What is the probability that he spends less than 3 hours playing the guitar during a given week?
4. Soon after he took oce in 1963, President Johnson was approved by 160 out of a sample of 200 Americans. With growing disillusionment over his Vietnam policy, by 1968 he was approved by only 70 out of a sample of 200 Americans.
(a) What is the 90% con dence interval for the percentage of all Americans who approved of Johnson in 1963? In 1968?
(b) What is the 90% con dence interval for the change?

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics