A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Related questions
Question
Transcribed Image Text:Consider the discrete random variable X given in the table below. Calculate the mean, variance, and
standard deviation of X.
13
15
20
P(X)
0.08
0.1
0.58
0.12
0.12
u =
o? =
What is the expected value of X?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps with 2 images
Knowledge Booster
Similar questions
- 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)arrow_forwardFind 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.)arrow_forwardGentle 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…arrow_forward
- 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%arrow_forwardThe 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.arrow_forwardGentle 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.)arrow_forward
- 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?arrow_forwardX-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 3arrow_forwardThe 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 Parrow_forward
- 1.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 decimalarrow_forwardThe 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 runsarrow_forwardGentle 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). 92 86 81 105 100 112 86 90 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 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; right-tailedH0: μ = 85; H1: μ < 85; left-tailed H0: μ = 85; H1: μ ≠ 85; two-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 standard normal,…arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:9780134753119
Author:Sheldon Ross
Publisher:PEARSON