High school probability Uncovered: Discover the Secrets with Plainmath's Expert Help

When Tim Hortons used physical cups for their Roll up the Rim contest (before switching over to "digital cups") they printed the cups so that 1 out of every 6 cups would be a winner. If the winning cups are truly randomly spread throughout the country.
a) A person feels they are particularly unlucky when it came to buying Tim Hortons coffee and winning Roll up the Rim. They often tell the story about how they kept buying losing coffee cups until the 16th cup was their first winning cup. What is the probability that someone could purchase this many cups and only win on the 16th cup?

It is believed that 58% of Americans like to eat at restaurants every week. You interview 6 Americans and ask if they like to eat at restaurants every week. The random variable x represents the number of Americans that like to eat at restaurants every week.
Find the mean of the binomial distribution. ${\displaystyle \mu =?}$
Find the standard deviation of the binomial distribution. ${\displaystyle \sigma =?}$
What is the probability that at least 1 of the Americans surveyed likes to eat at restaurants every week? Provide an answer to 4 decimal places.

A car has five traffic lights on its route. Independently of other traffic lights, each traffic light turns red as the car approaches the light (and thus forces the car to stop at the light) with a probability of 0.4.
a Let K he a random variable that denotes the number of lights at which the car stops with parameters (5,0.4). What is the PMF of K?
b. What is the probability that the car stops at exactly two lights?
c. What is the probability that the car stops at more than two lights?
d.What is the expected value and the variance of K?

In a survey of college graduates, 61% reported that they entered a profession closely related to their college major. If 8 college graduates are randomly selected, use the binomial distribution to find the probability of each item.
a) Getting exactly ${\displaystyle 3(x=3)}$ that entered a profession closely related to their major.
b) Getting 3 or fewer ${\displaystyle (x\le 3)}$ that entered a profession closely related to their major.
c) Getting at least one ${\displaystyle (x\ge 1)}$ that entered a profession closely related to their major.

During a visit to a local zoom, students either roam around the zoo solo or with thier friends. It is seen that 20% of the students roam around with thier freinds during a visit to a local zoo
In a sample of 6 studentsfind the prob that alteast 2 will roam around with thier friends in the zoo
use binomial prob function in excel to solve the question

Consider a share that is modelled by a binomial random variable. The probability that the share increases in value by 20¢ in one month is 0.6. The probability that it decreases in value by 20¢ in one month is 0.4. The share is held for 5 months then sold. Let X denote the number of increases in the price of the share over the 5 months. В (п,
(a) What is n and p if ${\displaystyle X\sim B(n,p)?}$
(b) Find ${\displaystyle E\left(X\right)\text{and}\sigma \left(X\right)}$.
(c) Let Y be the random variable which models the change in share price. Then ${\displaystyle Ү-0.2X-0.2(n-X)}$ because 0.2X is the total increase in share price and ${\displaystyle 0.2(n-X)}$ is the total decrease in share price. Simplify the expression for Y in terms of X. Then using (b), find E(Y) and ${\displaystyle \sigma \left(Y\right)}$.

According to the American Medical Association, about 36% of all U.S. physicians under the age of 35 are women. Your company has just hired eight physicians under the age of 35 and none is a woman. If a group of women physicians under the age of 35 want to sue your company for discriminatory hiring practices, would they have a strong case based on these numbers? Use the binomial distribution to determine the probability of the company’s hiring result occurring randomly, and comment on the potential justification for a lawsuit.
(Round your answer to 4 decimal places.)
Probability of hiring result occuring randomly: enter the probability of the company’s hiring result occurring randomly

A batch of 400 LEDS contains 7 that are defective. This is known to be the long-term average for the production. The company sells boxes with 50 LEDS in each box.
(a) What is the probability there are 1 or more defective bulbs in a box?
(b) If three LEDS are selected at random from a box, what is the probability that the third one selected is defective given that the first one selected was not defective and the second one selected was defective?
(c) Boxes are returned if 3 or more are defective. What is the probably a box will be returned?

A component may come from any one of three manufacturers with probabilities ${\displaystyle p1=0.25,p2=0.50,\text{and}p3=0.25}$. The probabilities that the components will function properly are a function of the manufacturer and are 0.1, 0.2, and 0.4 for the first, second, and third manufacturer, respectively.
a. Compute the probability that a randomly chosen component will function properly.
b. Compute the probability that three components in series randomly selected will function properly

In an assembly of 200 people there approximately 2% of them are civil engineers. If we randomly select five people, what is the probability of them being civil engineers?

Imagine that the probability that a random person will receive a phone call during this exam is approximately 16%. Let's assume that there are 24 students taking this exam. What is the probability that at least one student will receive a phone call during the exam?

In a particular country on the African continent, 35% of the population is estimated to have at least one smart phone. If a small sample of 40 people is selected from the population for a statistical investigation, Use the Binomial distribution to estimate the probability of the number of people in the sample that have at least one smart phone is;
a) at most 15;
b) more than 12 but fewer than 18;
c) exactly equal to the mean of the distribution

You have 165 observations of experiments in which a subject tried to guess which of 4 videos a psychic "sender" was watching in another room. Of the 165 cases, 61 resulted in successful guesses. What sort of distribution is this from? What are the sample mean and standard deviation? Compute a 95% confidence interval for the probability of a successful guess. Does this convince you of ESP? Why or why not?

Can a binomial random variable X have a mean ${\displaystyle =7}$ and the variance ${\displaystyle =11}$. Why or why not?

The state runs a lottery once every week in which six numbers are randomly selected from 16 without replacement. A player chooses six numbers before the state’s sample is selected. The player wins if all 6 numbers match. If a player enters one lottery each week, what is the probability that he will win at least once in the next 200 weeks? Report answer to 3 decimal places.

What does it mean 5C3? Solve, please.

Plastic drinking straws are manufactured to fit into drinks cartons which have a hole in the top. A straw fits into the hole if the diameter of the straw is less than 3 mm. The diameters of the straws have a normal distribution with mean 2.6 mm and standard deviation 0.25 mm.
(a) A straw is chosen at random. Find the probability that it fits into the hole in a drinks carton.
(b) 500 straws are chosen at random. Use a suitable approximation to find the probability that at least 480 straws fit into the holes in drinks cartons.

A professor has learned that two students in her class of 15 will cheat on the exam. She decides to focus her attention on five randomly chosen students during the exam.
a. What is the probability that she finds at least one of the students cheating? (Round your final answers to 4 decimal places.) Probability ?
b. What is the probability that she finds at least one of the students cheating if she focuses on seven randomly chosen students? (Round your final answers to 4 decimal places.) Probability ?

Garam Doe’s daily chores require making 10 round trips by car between two towns. Once through with all ten trips, Mr. Doe can take the rest of the day off, a good enough motivation to drive above the speed limit. Experience shows that there is a 44% chance of getting a speeding fine on any round trip. What is the probability that the day will end with at most one speeding tickets (one or less)