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A sample of n=400 observations is drawn from a population with mean μ=1,000 and σ=400. Find the following probabilities:
p(970<x<1030) is
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- A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events. B = individual purchased the product S = individual recalls seeing the advertisement BnS = individual purchased the product and recalls seeing the advertisement The probabilities assigned were P(B) = 0.20, P(S) = 0.40, and P(BS) = 0.12. a. What is the probability of an individual's purchasing the product given that the individual recalls seeing the advertisement (to 1 decimal)? Does seeing the advertisement increase the probability that the individual will purchase the product? - Select your answer - As a decision maker, would you recommend continuing the advertisement (assuming that the cost is reasonable)? - Select your answer - + b. Assume that individuals who do not purchase the company's soap product buy from its competitors. What would be your estimate of the company's market share (to the…Given a sample with a mean of 151 and a standard deviation of 27, find the probability that a randomly selected value from the sample will be less than 187.0. Round your answer to 3 decimal places, e.g. 0.194. Pr(X < 187.0)The mean was found to be u = 70 so now we need to find the standard deviation o. The standard deviation is calculated as follows where n is the sample size, 350, and p is the probability of a success, 0.2. Find the standard deviation. V np(1 – p) O = V 350( )(1 – 0.2)
- The heights of NBA players are normally distributed, with an average height of 6'7" (i.e. 79 inches), and a standard deviation of 3.5". You take a random sample of 8 players, and calculate their average height. What is the probability that this sample average is between 78 and 81 inches?A small retail store has customers whose ages are normally distributed, with a mean of 37.5 and a standard deviation of 7.6. What is the probability that a randomly selected customer is younger than 25 years old? Round your answer to three decimal places, e.g. 0.685.A health expert evaluates the sleeping patterns of adults. Each week she randomly selects 40 adults and calculates their average sleep time. Over many weeks, she finds that 5% of average sleep time is less than 3 hours and 5% of average sleep time is more than 3.4 hours. What are the mean and standard deviation (in hours) of sleep time for the population? (Round "Mean" to 1 decimal places and "standard deviation" to 3 decimal places.) Mean Standard deviation
- Given a sample with a mean of 57 and a standard deviation of 14, find x such that Pr(X > x) = 0.715. Round your answer to two decimal places, e.g. 22.96.Suppose that SAT scores among U.S. college students are normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that a randomly selected individual from this population has an SAT score between 500 and 600? 0.1587 0.3173 0.4207 0.3413The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,642. Assume the standard deviation is o = $2,400. (a) What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean for each of the following sample sizes: 20, 60, 100, and 300? (Round your answers to four decimal places.) sample size n = 20 sample sizen = 60 sample sizen = 100 sample size n = 300 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? A larger sample has a standard error that is closer to the population standard deviation. A larger sample increases the probability that the sample mean will be within a specified distance of the population mean. A larger sample increases the probability that the…
- A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events. B = individual purchased the product S = individual recalls seeing the advertisement BNS = individual purchased the product and recalls seeing the advertisement The probabilities assigned were P(B) = 0.20, P(S) = 0.40, and P(BnS) = 0.12. %3D a. What is the probability of an individual's purchasing the product given that the individual recalls seeing the advertisement (to 1 decimal)? Does seeing the advertisement increase the probability that the individual will purchase the product? - Select your answer- As a decision maker, would you recommend continuing the advertisement (assuming that the cost is reasonable)? - Select your answer - b. Assume that individuals who do not purchase the company's soap product buy from its competitors. What would be your estimate of the company's market share (to the…The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large number of observations, the distribution of trout weights is normally distributed with a mean of402.7grams and a standard deviation of12.8grams. What is the probability that the mean weight for a sample of 42 trout exceeds405.5grams? a.0.4338 b.1.0 c.0.5 d.0.0778A NUMMI assembly line, which has been operating since 1984, builds 900 cars and trucks in a week. Generally, 10% of those cars are defective coming off the assembly line. What type of distribution does the event of having defective cars follow? What are the mean and standard deviation of this random event? (6 points) Can we apply the normal distribution to study this event? Check the conditions and answer the question. (6 points) Find the probability that the assembly line produces at least 825 cars, that are not defective and functional, in a week. Graph the situation, shade in the area to be determined, and find the probability. (6 points)