Consider the discrete random variable X given in the table below. Calculate the mean, variance, and standard deviation of X. X 13 15 20 P(X) 0.08 0.1 0.58 0.12 0.12 %3D O = What is the expected value of X?
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- Assume the random variable X is normally distributed, with mean μ=42 and standard deviation σ=9. Find the 9th percentile. The 9th percentile is ______ (Round to two decimal places as needed)Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n=124, p=0.53 The mean, μ, is enter your response here. (Round to the nearest tenth as needed.) The variance, σ2, is enter your response here. (Round to the nearest tenth as needed.) The standard deviation, σ, is enter your response here. (Round to the nearest tenth as needed.)Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 93 87 81 104 98 110 85 90 The sample mean is x ≈ 93.5. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that σ = 12.5. The mean glucose level for horses should be μ = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use α = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ = 85; H1: μ < 85; left-tailedH0: μ = 85; H1: μ ≠ 85; two-tailed H0: μ = 85; H1: μ > 85; right-tailedH0: μ > 85; H1: μ = 85; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n…
- Suppose x is a normally distributed random variable with mean u =0 and standard deviation o = 1. Find the probability that x < 0.64. O 73.89% 76.11% 23.89% O 26.11%The weight of grapefruits produced by an orchard is normally distributed, with a mean weight (μ) of 450g and a standard deviation of 50g. We randomly select a sample of 120 grapefruits from the orchard. Q.3.1.1 Compute the standard error.Q.3.1.2 What is the probability that the average weight of the grapefruits in the sample will lie between 445g and 460g? Interpret your answer.Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 95 86 82 105 97 112 86 89 The sample mean is x ≈ 94.0. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that σ= 12.5. The mean glucose level for horses should be μ= 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 0.05. (a) Compute the z value of the sample statistic. (Round your answer to two decimal places.) (b) Find (or estimate) the P-value. (Round your answer to four decimal places.)
- Storm damage can occur to homes in any given year, with the amount of damage varying randomly from year to year. Let X represent the dollar value of storm damage in a given year. It is known that in 95% of the years, X = $0, while in 5% of the years, X = $20,000. What is the expected value and standard deviation of the damage in any given year?The life of a certain type of interconnection material for an electronic device in years is denoted by x which follows the Weibull distribution. The parameters for the distribution are a=0.03 and B=2. What is mean of the random variable x? 50 6.3 33.3 5.1X-X Z= Z-score: Variance: σ ²=Σ(x-4)²P For questions 1 - 4, answer the questions about discrete random variables. Find the mean of the discrete random variable with the probability distribution below. Find the mean of the discrete random variable with the probability distribution below. X 1 2 3 4 5 X 3 4 5 6 7 P(x) 0.3 0.2 0.1 0.3 0.1 P(x) 0.1 0.2 0.3 0.15 0.25 1 2 Find E(X) for the discrete random variable with the probability distribution below. Find the mean of the discrete random variable with the probability distribution below. X 0 2 4 6 8 X 1 4 5 6 8 P(x) 0.1 0.1 0.1 0.2 0.5 P(x) 0.2 0.2 0.2 0.3 0.1 3
- The lifetime of a certain residential air conditioner is normally distributed with a mean of 20 years and a standard deviation of 2 years. Find the probability that if one of these air conditioners is randomly selected, it will last between 19 years and 19.5 years. DII 00.093 O 0.401 00.309 00.290 O None of these Submit Question 4 R V F4 % 5 T G F5 6 Y H N F6 & 7 J 8 M PrtScn K O Home 9 End 0 F10 P1.Find the expected value E(X) 2.find the variance 3.find standard deviation 4.find the value of P(X<8) round all answers to one decimalThe answer choices for expected value of x is E(X): 0.561 0.531 0.550 0.697 The answer choices for the standard deviation of the random variable X, denoted σ,: 0.80.60.70.9 and which player is more likely to help the team score runs
