Consider a geometric distribution with parameter p. (a) Find the method of moments estimator for p. (b) Find the MLE for p.
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- Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ= 1.1 kg and a standard deviation of σ = 4.4 kg. Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is 0.2658. (Round to four decimal places as needed.) b. If 9 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg. The probability is (Round to four decimal places as needed.)The first method of moments equation uses the first sample moment about the mean a. True b. FalseCX K Assume that women's heights are normally distributed with a mean given by μ = 62.6 in, and a standard deviation given by a = 2.4 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 63 in. (b) If 42 women are randomly selected, find the probability that they have a mean height less than 63 in. View an example @ 2 F2 W S (a) The probability is approximately. (Round to four decimal places as needed.) X H mand # 3 Ask my instructor 80 F3 E D C $ 4 a F4 R F 07 dº V T G 6 MacBook Air B FO Y H & 7 F7 Ⓒ U N * 8 31 F8 1 M ( 9 K F9 O < I H ) O L F10 P command Clear all . V - ... I F11 { + [ = Check ans ? option 11 Show A F12 }
- Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.50 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit 1 upper limit 2 margin of error 3 (b) What conditions are necessary for your calculations? (Select all that apply.) n is large the distribution of weights is normal σ is known the distribution of weights is uniform σ is unknown (c) Interpret your results in the context of this problem. 1% of the intervals created using…The calibration of a scale is to be checked by weighing a 11 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? Ho: H = 11 Ha: u + 11 Ho: H + 11 H3i H 11 a (b) With the sample mean itself as the test statistic, what is the P-value when x = 10.83? (Round your answer to four decimal places.) What would you conclude at significance level 0.01? Conclude that the true mean measured weight differs from 11 kg. Conclude that the true mean measured weight is the same as 11 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 11.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 10.9? (Round your answer to…Let T represent the lifetime in years of a part which follows a Weibull distribution with shape 2 and scale 5. (a) What is E(T )? Make sure to simplify the gamma function in terms of pi.(b) What is V(T )? Make sure to simplify the gamma function in terms of pi.
- Enter a value for π. A die is rolled until it shows 6. Denote the number of times it was rolled by X. Compute: E(X): Standard deviation of X: (enter at least 3 decimal places).The position of a point A is defined from a point of observa- tion O by distance OA = D, and the angular deviation from a reference line OB. The mean error in estimating the distance is 100k per cent of the distance; the mean error in estimating the angular deviation is & radians. The error made in representing the point A on a chart obeys a normal tircular distribution with mean deviation r; the error in the position of the point O also obeys a normal circular distribution law with mean deviation R. Find the compound distribu- tion characterizing the error in position resulting from the representation of point A on the chart. How will the probability that point A lies in a rectangle of size 100 x 100 sq. m. change if D decreases from 20 to 10 km. (r = 20 m., R 40 m., & = 0.003, k 0.005) ? =A variable of two populations has a mean of 49 and a standard deviation of 14 for one of the populations and a mean of 54 and a standard deviation of 15 for the other population. a) For independent samples of sizes 34 and 45, respectively, find the mean and standard deviation of ₁ - 2. mean: standard deviation: b) Can you conclude that the variable 1 T2 is approximately normally distributed? (Answer yes or no) answer:
- Interstate Speeds It has been reported that the standard deviation of the speeds of drivers on Interstate 75 near Findlay, Ohio, is 8 miles per hour for all vehicles. A driver feels from experience that this is very low. A survey is conducted, and for 29 drivers the standard deviation is 9.1 miles per hour. At =α0.05, is the driver correct? Assume the variable is normally distributed. (a)State the hypotheses and identify the claim with the correct hypothesis.الموافق foo an exponentiaL distribution fx Cx jt) e.w. where u>o Write (Dankderive) meancespedoed V9lue) f.eECx)Cor A simple random sample of size 28 is drawn from a normal population whose standard deviation is a = 2. The sample mean is = 14.3. for Tutoring a.) Construct a 93% confidence level for µ. (Round answers to two decimal place.) Student rces margin of error: lower limit: e Drive upper limit: b.) If the population were not normally distributed, what conditions would need to be met? (Select all that apply.) large enough sample size n Oo is unknown Othe population needs to be uniformly distributed Do is known Uthe population needs to be normally distributed systematic sampling simple random sampte