4.42 For a mound-shaped, symmetric distribution, what is the probability that x falls into the interval u + 20?
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- The mean height of women in a country (ages 20−29) is 64.4 inches. A random sample of 60 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume σ=2.78. The probability that the mean height for the sample is greater than 65 inches is ___?The chance of an IRS audit for a tax return reporting more than 25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 20 year. Period assume each year is independent. a. give the distribution of X. X~B(__,__) b. how many audits are expected in a 20 year period? c. find the probability that a person is not audited at all. d. find the probability that a person is all the dead more than twice.Today, the waves are crashing onto the beach every 4.6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a uniform distribution from 0 to 4.6 seconds. Round to 4 decimal places where possible. The probability that the wave will crash onto the beach between 0.9 and 3.7 seconds after the person arrives is P (0.9 <x<3.7)=____ The probability that it will take longer than 1.22 seconds for the wave to crash intoned the beach after the person arrives is P(x>1.22) =_____ Suppose that the person has already been standing arc thr shoreline for 0.1 seconds without a wave crashing in. Find the probability that’s it will tale back between 2 and 3 second and for the wave Tovar’s crash onto the shoreline ________
- on average, research shows that people gain one to three pounds over the winter months. Let x denote how much weight a person gain over the winter months. suppose that x followed a uniform distribution, what is the probability a person will gain between 1.2 and 2.3 Ilbs during the winter months?Assume that the normal distribution can be used to approximate the following binomial distribution question. A survey of adults found that 6% say their favorite sport is auto racing. You randomly select 400 adults and ask them to name their favorite sport. Complete parts (a) and (b). (a) Find the probability that the number of people who say auto racing is their favorite sport is at most 30. (b) Find the probability that the number of people who say auto racing is their favorite sport is more than 33. (Round to four decimal places as needed.)Q8
- Q1: let an experiment consist of tossing a pair of unbiased dice. Let X be a random variable indicating the sum of the two faces. find: 1- Sample space. 2- P (X= x) 3- 3- Mathematical Expectation. 4- Does the conjugation represent a normal distribution?Peter the Anteater sometimes walks around UCI's campus. The probability that you see Peter during any given day is 0.0689. Let X be the number of days you walk through campus before you see Peter the Anteater. (a) What distribution does X follow? What assumptions do you need to make to say that X has this distribution? (b) Compute the expected number of weeks from now until you see Peter the Anteater. (Make sure to identify the units.) (c) What is the variance and standard deviation of the number of days until you see Peter the Anteater? Provide the appropriate units and answer rounded to 3 decimal places. (d) What is the probability that when you see Peter the Anteater it is during your midterms in about 3 weeks, or 21 days? Round your answer to 3 sig figs.Time spent using e-mail per session is normally distributed, with u= 11 minutes and a = 3 minutes, Assume that the time spent per session is normally distributed. Complete part (a) through (d). a. If you select a random sample of 50 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes? 0.363 (Round to three decimal places as needed.) b. If you select a random sample of 50 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes? O (Round to three decimal places as needed.)
- According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York City has a 90% chance of arriving on time on a randomly selected day. Suppose this claim is true. Choose 6 days at random. Let Y = the number of days on which the train arrives on time. What is P(Y = 4)? Interpret this value. (0.90)4 (0.10)². There is a 0.66% probability that exactly 4 of the 6 trains arrive on time. (0.90) ¹ (0.10)². There is a 0.66% probability that at least 4 of the 6 trains arrive on time. This probability cannot be calculated because this is not a binomial setting. O()(0.90)+ (0.10)². There is a 9.84% probability that at least 4 of the 6 trains arrive on time. O()(0.90)4 (0.10)². There is a 9.84% probability that exactly 4 of the 6 trains arrive on time.Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $4.30 per gallon and an upper bound of $4.50 per gallon. What is the probability a randomly chosen gas station charges more than $4.35 per gallon? Multiple Choice 1.0000 0.20000.7500 0.8834[O] Uniform Distribution: Q68. A discrete random variable x follows uniform distribution and takes only the values 6, 8, 11, 12, 17. The probability of P x (a) 1/5 (b) 3/5 8) is: (c) 2/8 (d) 3/8