According to a study, 39% of adult Americans believes that marriage is now obsolete. A random sample of 500 adult Americans is surveyed. The proportion of adult Americans in the sample who believe marriage is obsolete is the sample proportion p ̂. Describe the sampling distribution of p ̂. What is the probability that in a random sample of 500 adult Americans less than 38% believe that marriage is obsolete?

Q: 2016, 48.3% of college students voted.  What is the probability of getting 40 or fewer students who…

A: Number of trail n=100Probability of success p=0.483

Q: A disease has a prevalence of 11%. A diagnosis has 85% probability of correctly identifying the…

A: Let D=The Person has the disease. Dc=The person doesn't have the disease. P=The person is tested…

Q: 30% of the firm's orders are from first time customers. Consider random sample of 84 orders. Find…

A: Given,n=84p=0.30

Q: ABC Interactive survey stated that 25% of employees said that their company is loyal to them. Ten…

A:

Q: A recent survey found that 2.9% of adults are allergic to shellfish, while 1.8% are allergic to…

A: Given that the percentage of allergic to shellfish is 2.9%, the percentage of allergic to peanuts is…

Q: The coach of a running team thinks that 45% of athletes can run a mile in under 7 minutes. A simple…

A: Given problem Given that   The coach of a running team thinks that 45% of athletes can run a mile…

Q: In a recent year, 13% of businesses have eliminated jobs. If 6 businesses are randomly sampled, what…

A: Let us denote X=the number of businesses that have eliminated jobs. n=sample size=6 p=probability of…

Q: A research firm conducted a survey to determine the average amount of money consistent smokers spend…

A: We have given that,  Let X be a random variable from normal distribution with mean(μ) = 20 and…

Q: Based on surveys, 97% of students own cell phones.  What is the probability that 10 randomly…

A: Given,p=0.97n=10X=no.of students own cell phones.X~Binomial(n=10 , p=0.97)P(X=x)=Cxn px(1-p)n-x ;…

Q: According to government data, the probability that an adult was never in a museum is 15%. In a…

A: Given,n=10p=0.15q=0.85A random variable X~Binomial(n=10 , p=0.15)P(X=x)=Cx100.15x0.8510-x    ;…

Q: A study showed that 64.5​% of occupants involved in a fatal car crash wore seat belts. Of those in…

A: Solution: Let A be the event that  occupants involved in a fatal car crash wore seat belts. P( A)=…

Q: According to an article published at heart.org in 2015 regarding a variety of US health data: Given…

A: Solution: Given information: Let A  be the event that someone in the US has a first time  heart…

Q: Based on historical data, your manager believes that 26% of the company's orders come from…

A: Introduction:Here, the suggested population proportion, π = 26% = 0.26.The sample size, n = 112.The…

Q: The test statistic is 1.26. Which of the following is the best interpretation of this value?

A: Given that  Test statistic is given by Z = 1.26

Q: A courier service company wishes to estimate the proportion of people in various states that will…

A: number of samples, n = 330 true proportion, p = 0.05 Let, p^ be the sample proportion.  Hence p^…

Q: Find the probability that more than 20% of the sample are from poverty-level households.

A: Given,sample size(n)=300sample proportion(p^)=0.22

Q: Based on a smartphone​ survey, assume that 51​% of adults with smartphones use them in theaters. In…

A:

Q: What is the probability of selecting a sample with the proportion of females being 0.56 or greater?

A: here p =  proportion of female in US =  0.51  n = 500

Q: A study showed that ​69.7% of occupants involved in a fatal car crash wore seat belts. Of those in a…

A:

Q: According to a study, 20% of corporate officers are women. Suppose that you select a random sample…

A:

Q: In a survey of 500 individuals, it was found that 60% of them prefer tea over coffee. Of those who…

A: Answer: To find the probability, we need to calculate the proportion of individuals who prefer tea…

Q: Based on a smartphone survey, assume that 56% of adults with smartphones use them in theaters. In a…

A: Given information- We have given a problem of binomial distribution. We have given that 56% of…

Q: Based on a​ poll, among adults who regret getting​ tattoos, ​17% say that they were too young when…

A:

Q: In 2017, 39.2% of the total email messages is spam. If 59 email messages from 2017 are randomly…

A: From the given information ,39.2% of the total email messages is spam .ie, P(success) = p = 39.2% =…

Q: A market research organization surveyed 102 people and found that 73 of them would like more…

A:

Q: According to a survey, 36.7% of people who visit Disney World have children under 18 in their…

A: A: People who visit Disney World have children under 18 in their household   B:  Household with…

Q: According to a 2018 survey, 74 percent of employed young adults expect to bring work on a vacation…

A:

Q: Within what interval would you expect the sample mean to fall, with 98 percent probability?

A:

Q: Last Fall Semester, 36% of freshmen who applied for football season tickets did not receive tickets…

A: Obtain the probability that more than 40% of those sampled did not receive tickets for all home…

Q: The centers for disease control reported that 16% of college aged individuals used vapes in…

A: Given information Probability of using vapes = 0.16 No of individuals n = 750 Probability that less…

Q: Based on a smartphone​ survey, assume that 41​% of adults with smartphones use them in theaters. In…

A: See the handwritten solution

Q: Based on a​ poll, among adults who regret getting​ tattoos, 23% say that they were too young when…

A: Givenp=0.23n=10x~Binomial(n=10,p=0.23)P(X=x)=(nx)×px×(1-p)n-x     ; x=0,1,...,n

Q: Based on a smartphone​ survey, assume that   42​% of adults with smartphones use them in theaters.…

A:

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.