A random variable X follows a Normal distribution with mean u = 40.8 and standard deviation o = 6.9. Which of the following gives th expectation E[X²]? O A. 1712.25 O B. 1664.64 O C. 47.61 O D. 281.52 O E. Insufficient information to calculate E(X^2)
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- A random sample of 90 eighth grade students' scores on a national mathematics assessment test has a mean score of 288. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 36. At α = 0.08, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. A. Ho: μ = 280 (claim) Ha:μ>280 Ho:μ≤280 Ha: μ> 280 (claim) B. Ho: μ = 280 P-value = (b) Find the standardized test statistic z. z = 2.11 (Round to two decimal places as needed.) (c) Find the P-value. E. Ho: μ≤280 (claim) Ha:μ>280 Ha: μ> 280 (claim) (Round to three decimal places as needed.) C. Ho: μ ≥280 (claim) Ha:μ< 280 F. Ho: μ< 280 H₂:μ ≥280 (claim)Suppose X is a non-standard normal variable, with a mean of 145, and std deviation of 10 (i.e. X~N(145,10)). You have an observation (z) on a standard normal scale (i.e. Z~N(0,1)). If z = 0.72, what is it on an X scale? Express your answer to two decimal places (ex: 123.45).A random sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 38. At α = 0.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. O A. Ho: ≤280 (claim) H₂:μ>280 O D. Ho: μ≤280 Ha: μ> 280 (claim) B. Ho: μ280 OF. Ho: μ = 280 H₂: µ>280 (claim)
- Q2: Suppose the current measurements in a strip of wire are assumed to follow a normal distribution with a mean of 10 milliamperes and a variance of 4 (milliamperes)² 1- What is the probability that a measurement will exceed 13 milliamperes? 2- what is the probability that a current measurement is between 9 and 11 milliamperes?Suppose X is a non-standard normal variable, with a mean of 122, and std deviation of 15 (i.e. X~N(122,15)). You have an observation (z) on a standard normal scale (i.e. Z~N(0,1)). If z = -1.39, what is it on an X scale? Express your answer to two decimal places (ex: 123.45).A random sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 38. At α = 0.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. O A. Ho: μ≤280 (claim) H₂:μ>280 O D. Ho: μ≤280 Ha: μ> 280 (claim) O B. Ho: μ280 OF. Ho: μ = 280 Ha: μ>280 (claim)
- The lifetime of a specific species of mammal is normally distributed with mean μ=22 years and standard deviation σ=4 years. We pick randomly a mammal from the above species. What is the probability the mammal lives: Less than 28years? Between 20 years and 28 years? Exactly 67% of the mammal of this species live at most y What is the value of y?H0:μ=41.92H0:μ=41.92H1:μ≠41.92H1:μ≠41.92Your sample consists of 43 subjects, with a mean of 42 and standard deviation of 1.56.Calculate the test statistic, rounded to 2 decimal places. t=Find the inflection points of a normal random variable with mean of u (Mu) and a standard deviation of sigma
- Suppose X is a non-standard normal variable, with a mean of 190, and std deviation of 7 (i.e. X~N(190,7)). You have an observation (z) on a standard normal scale (i.e. Z~N(0,1)). If z = -1.15, what is it on an X scale? Express your answer to two decimal places (ex: 123.45).A population of values has a normal distribution with u = 10.3 and o = random sample of size n = 199. 89.3. You intend to draw a What is the mean of the distribution of sample means? Hx = E(X) What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) SD(X)