(iii) In this question, you may use the table of areas under the standard normal curve, which is supplied to you. A random variable X is normally distributed with a mean of 60 and a standard deviation of 12. Find: (a) P(54 s X s75) . (b) the value of k such that P(X 2k)=0-063
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- Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with ? = 2.2, ? = 1.5, and ? = 0.5. P(1 < X < 2)? P(X > 1.5)? What are the mean and standard deviation of X?F(144) Generation Y has been defined as those individuals who were born between 1981 and 1991. A 2010 survey by a credit counseling foundation found that 60% of the young adults in Generation Y pay their monthly bills on time. Suppose we take a random sample of 190 people from Generation Y. Question content area bottom Part 1 The distribution of p is a aproximately normal. Calculate the standard deviaiton of p. σp=enter your response here (Round to four decimal places as needed.) What is the probability that between 106 and 120 of them will pay their monthly bills on time? P(Between 106 and 120 of them will pay their monthly bills on time)=enter your response here (Round to four decimal places as needed.)The probability distribution of X, the number of imperfections for every 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by 1 2 3 4 f(x) 0.41 0.37 0.17 0.05 0.01 find the mean and variance of X. (10 pts)
- Let x represent the dollar amount spend on supermarket impulse buying in a 10-minute unplanned shopping interval. The mean of this distribution is µ=$25 and the standard deviation is =$10. If we assume the x distribution is approximately normal: (1) What is the probability that a randomly selected shopper will spend between $18 and $22? (1) Consider a random sample of n = 100 shoppers. What is the probability that is between $18 and $22? (2) State two different ways we know the distribution from part (b) is normally distributed.The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution ? = 0.5 and ? = 0.289. (a) Let x be the sample mean waiting time for a random sample of 17 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.) ?x = ?x = (b) Answer part (a) for a random sample of 45 individuals. (Round your answers to three decimal places.) ?x = ?x = (c) Draw a picture of the approximate sampling distribution of x when n = 45. A graph has a horizontal axis with values from approximately −3.5 to 3.5. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0 on the horizontal axis, then decreases and exits the graph on the…Withdrawal symptoms may occur when a person using a painkiller suddenly stops using it. For a special type of painkiller, withdrawal symptoms occur in 4% of the cases. Consider a random sample of 2400 people who have stopped using the painkiller. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where p is the proportion of people in the sample who experience withdrawal symptoms. (b) Find the standard deviation of (c) Compute an approximation for P(p <0.05), which is the probability that fewer than 5% of those sampled experience withdrawal symptoms. Round your answer to four decimal places.
- A normal distribution has a mean of=100 with a SD= 20 . If one score is randomly selected from this distribution. What is the probability that the score will have a value between X=100 and X=130? NOTE: Using the z-score table attachedThe time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution ? = 0.5 and ? = 0.289. (a) Let x be the sample mean waiting time for a random sample of 12 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.) ?x = ?x = (b) Answer part (a) for a random sample of 40 individuals. (Round your answers to three decimal places.) ?x = ?x =Women's heights are normally distributed with a mean given by u = 63.6 in. and a standard deviation given by o = 2.5 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 62.6 in. Enter a number correct to 4 decimal places: (b) If 52 women are randomly selected, find the probability that they will have a mean height less than 62.6 in. Enter a number correct to 4 decimal places:
- nN(dp) is define as the “number distribution function” , where dp is the particle diameter. Assume nN(dp) is a normal distribution with a mean of 10 µm and a standard deviation of 2 µm. The total number concentration of particles of all sizes is 10,000 particles cm-3. What is the number concentration of particles in the size range 10 µm and 14 µm?Which of the following statement is INCORRECT? If Y, follows the standard normal distribution and Y, follows a chis-square distribution with degrees of freedom n, then nY/Y t distribution. If X1,.., Xn is a random sample from a normal population with population mean 1 and variance 1, then (X -1) + (X - 1 (X, - 1) follows a chi-square distribution with degrees of freedom n. If X,..., Xn is a random sample from a normal distribution with population mean 0 and a known variance o, then must follow a distribution, where X denotes the sample mean and S denotes the sample standard deviation. If T follows at distribution with degrees of freedom n, then T must follow an F distribution with degrees of freedom 1 and n.