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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .Suppose you play a coin toss game in which you win $1 if a head appears and lose $1 if a tail appears. In the first 100 coin tosses, heads comes up 41 times and tails comes up 59 times. you toss the coin 200 more times (a total of 300 tosses), and at that point heads has come up 42% of the time. Is this change in the percentage of heads consistent with the law of large numbers? How many heads would you need in the next 100 tosses in order to break even after 400 tosses? Is this likely to occur? Select the correct choice and fill in the answer box to complete your choice.
- We ask a random sample of 1000 New Zealanders their opinion on whether New Zealand should become a republic with a president replacing the Queen as head of state and 350 answer ‘yes’. We are testing the following pair of hypotheses for the value of p, the true proportion of New Zealanders who think that New Zealand should become a republic with a president replacing the Queen as head of state: H0: p = 0.40 Ha: p > 0.40 Select the correct value (to 3 decimal places) of the z-test statistic for this sample from the list below. Select one: a.3.315 b.-3.227 c.-3.315 d.3.227Your internal body temperature T in °F is a Gaussian (μ =98.6, σ = 0.4) random variable. In terms of the Φ function, find P[T > 100]. Does this model seem reasonable?3.Suppose that you are interested in finding proportion of males that order cold brew at Starbucks. Starbucks states that 40% of males order cold brew on the regular. From a sample of 375 males at a local Starbucks, you observe that 165 ordered cold brew. You are then interested to find whether the proportion of males that order cold brew has changed c) Find the p-value. Round to four decimal places
- urgently please answer question 2 and 3 QUESTION 2 An experiment was conducted into car tyre wear by the department of Materials Science at Lowlands University, which it has been asked to carry out by a tyre company. The tyre company hascreated a new compound which it hopes will make tyres last much longer. Various levels of the compound were mixed in with rubber to make tyres. Apart from that, all the tyres were identical, with 16mm of tread when new. One hundred motorists chosen at random were given new tyres, and split into ten groups. After each motorist had completed 10,000 miles on the new tyres, the level of tread remaining was measured. The data recording the experiment is set out in the table below. You have been asked to use correlation analysis to see if there is a relationship between the percentage of the new compound and the wear on the tyres. Identify appropriate x and y variables, stating clearly which variable is the “x” variable and which is the “y” variable…SI jinx Players in any sport who are having greatseasons, turning in performances that are much betterthan anyone might have anticipated, often are picturedon the cover of Sports Illustrated. Frequently, their performances then falter somewhat, leading some ath-letes to believe in a “Sports Illustrated jinx.” Similarly, it is common for phenomenal rookies to have less stel-lar second seasons—the so-called “sophomore slump.” While fans, athletes, and analysts have proposed many theories about what leads to such declines, a statisti-cian might offer a simpler (statistical) explanation. Explain.The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .