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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- Suppose that the times taken for germination for cauliflower seeds are normally distributed with a mean of 7 days. Suppose also that exactly 85%of the cauliflower, seeds germinate in 6.1days or more. Find the standard deviation of times taken for germination for cauliflower seeds. Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.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)100 specimens are tested in determining the life cycle of a certain type of crank shaft which is used in a particular brand of car engine. The tests have shown an average life cycle of μ=44 Gc (1 Gc = 1 gigacycles = 109 cycles) and a standard deviation of σ=33x10-1 Gc. 200 hundred thousand cars using that engine have been sold and are on the traffic. After what number of Gigacycles would you expect 7 % of the shafts broken down?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).
- 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=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).