A survey showed that a majority of Americans plan on doing their holiday shopping online because they don’t want to spend money on gas driving from store to store. Suppose we have a group of 10 shoppers; 7 prefer to do their holiday shopping online and 3 prefer to do their holiday shopping in stores. A random sample of 3 of these 10 shoppers is selected for a more in-depth study of how the economy has impacted their shopping behavior.a) What is the probability that exactly two prefer online shopping?b) What is the probability that the majority (either two or three) prefer shopping online?

At a certain large company, the floor manager reviewing inventory and production. She ultimately comes to the decision that a product should be continued if it sold 150,000 times over the previous year. In addition, the product is considered “popular” if it receives at least 100 mentions by the local press over the past year. An analyst is hired to help with the analysis.  The analyst determines that the probability of sales exceeding 150,000 was 0.331, the probability of 100 or more mentions was 0.162, and the probability that a product both sold 150,000 items, and was also ‘popular’ is 0.064. What is the probability that a randomly selected product either sold the requisite 150,000 items, or that it is ‘popular’? Again, phrase your answers in terms of probability variables (e.g. P(X) = ...,  P(Y)=... etc.) If we are told that an item has indeed reached the threshold of 100 mentions in the press, what is the probability of it selling 150,000 times?  Thought Question: Where would the…

5. A manufacturer of cell phones purchases batteries from a vendor. It is not uncommon to receive defective batteries from this vendor, thus whenever a shipment is received, a sample of batteries is inspected. For this month's shipment, a random sample of 280 batteries is selected and each battery is inspected. If the proportion of defective batteries sampled is more than 1.5%, the entire shipment will be returned to the vendor. What is the probability that this month's shipment will be returned if the true proportion of defective batteries is 4%?

A study showed that in​ 1990, 47​% of all those involved in a fatal car crash wore seat belts. Of those in a fatal crash who wore seat​ belts, 46​% were injured and 26​% were killed. For those not wearing seat​ belts, the comparable figures were 43​% and 51​%, respectively. Find the probability that a randomly selected person who was unharmed in a fatal crash was not wearing a seat belt.

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 38 arrests last month, 21 were of males aged 15 to 34 years. Use a 1% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. LAUSE SALT (a) What is the level of significance? ← State the null and alternate hypotheses. OM P=0.7; M₁: P 5 and ng> 5. O The Student's t, since np> 5 and ng 5. O The Student's t, since np < 5 and ng < 5 O The standard normal, since np < 5 and ng < 5 What is the value of the sample test statistic? (Round your answer to two decimal places) - (C)…

Fewer young people are driving. In 1995, 63.9% of people under 20 years old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample of 1,200 people under 20 years old who were eligible to have a driver's license in 1995 and again in 2016.

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 yearst. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 38 arrests last month, 24 were of males aged 15 to 34 years. Use a 10% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: P = 0.7; H₁: p > 0.7 Ho: P = 0.7; H₁: P = 0.7 O Ho: P = 0.7; H₁: p 5 and nq > 5. O The Student's t, since np 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic.…

Do cat owners sleep better than those without cats? To help answer this question, a cat enthusiast obtained a random sample of 500 Canadians, each of whom answered two questions: 1. do you have a cat? (yes or no), 2. How well do you sleep? (good, neutral, bad). The dataset “CatSleep.xlsx” contains her findings.   Find the probability that a randomly selected Canadian is a bad sleeper and a cat owner. Find the probability that a randomly selected Canadian is a neutral sleeper or a cat owner. Find the probability that a randomly selected non-cat owner is a bad sleeper. That is, find the probability that a randomly selected Canadian is a bad sleeper, given they are not a cat owner Can you handwrite the solution?