Let X denote the mean of a random sample of size 128 from gamma distribution with 2, and B = 4. Approximate p(7
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- The focus of a human eye is measured in diopters. For a given person, the focus is modelled by a random variable with normal distribution N(μ, o) with mean and standard deviation o. Th focus under which eye correction for nearsightedness (myopia) is considered necessay is -3 diopters. The focus of a normal eye is larger than this value. Mr Y. got arrested for going through a stop sign, not wearing glasses. Throughout the exercise the threshold is set to 5%. Based on 3 measurements on Mr. Y, we have observed an average focus of -0.94. The hypothesis testing the policeman intends to do is H₁:> -3. a. Assuming the standard deviation known and equal to o = 1.6 diopters, the rejection region of the test statistics is (-∞, -1.645) (-1.96, 1.96) * (1.645, ∞)The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of two cracks per mile. 1. Determine the probability mass function of the number of cracks (X) in 5 miles of highway. 2. Calculate the mean and variance of XLet X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.25. What proportion of the values of X are less than 14? 0.945 0.933 0.625 None of these choices
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- Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score between negative 1.62 and 1.62. The probability is (Round to four decimal places as needed.)Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 111 pounds and a standard deviation of 37.8 pounds. Random samples of size 19 are drawn from this population and the mean of each sample is determined. 1₂ = 0 ...Assume all populations are normally distributed. A travel analyst claims that the mean price of a round trip flight from New York City to Los Angeles is less than $507. In a random sample of 55 round trip flights from NYC to LA, the mean price is $502. Assume the population standard deviation is $111. At α = 0.05, is there enough evidence to support the travel analyst’s claim?
- Let X represent the full height of a certain species of tree. Assume that X has a normal distribution with a mean of 115.4 ft and a standard deviation of 8.2 ft. A tree of this type grows in my backyard, and it stands 103.9 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. My neighbor also has a tree of this type growing in her backyard, but hers stands 119.5 feet tall. Find the nrobability that the ful height of a randomly selected tree is at least as tall as hers. Enter your answers as decimals accurate to 4 decimal places.An elevator can safely hold 3500 pounds. A sign in the elevator limits the passenger count to 15. If the adult population has a mean weight of 180 pounds with a 25-pound standard deviation, how unusual would it be, if the central limit theorem applied, that an elevator holding 15 people would be carrying more than 3500 pounds? Note. Use pnorm which is the normal distribution function of R.The lengths of nails manufactured at a factory are normally distributed with a mean length of 4.43 cm and a standard deviation of 1.41 cm. For quality control purposes, a random sample of 14 nails is chosen once per day, and measured. Let X be the random variable representing the mean length of the nails. A. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X is approximately normal with a mean of _______cm and a standard error of the mean________cmb. Find the z-score associated to a sample with a mean of 4.56 cm, using the sampling distribution. Round your answer to two decimal places. ______c. Find the probability that a randomly selected sample of 14 nails has a mean length higher than 4.56 cm. Round your answer to 4 decimal places.________
