Use the table to answer to find the probabilities below. P(2.2 < x< 3.8) = P(x > 2.72) =
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- 1) The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with σ = 0.32 and that x = 5.21. (Use α = 0.05.) What value of n is required to satisfy α = 0.01 and β(5.6) = 0.01? (Round your answer up to the next whole number.) 2) Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 7. The hypotheses H0: μ = 74 and Ha: μ < 74 are to be tested using a random sample of n = 25 observations. The number of standard deviations (of X) below the null value x = 72.3 is 1.21. If x = 72.3, the conclusion using α = 0.003 : z = -1.21 P-value = 0.1123 If the test procedure with α = 0.003 is used, what n is necessary to ensure that β(70) = 0.01? (Round your answer up to the next whole number.)3.59 3.59 4.79 3.56 3.55 3.71 3.65 3.6 3.75 3.56 3.57 3.59 3.55 3.99 4.15 3.66 3.63 3.73 3.61 3.57 1. Until five months ago, suppose the average weekly gas price had remained stable around $3.55, but a shock to supply seemed to push prices higher thereafter. Let’s test whether this is so using our data. 2. Develop the H0 and Ha hypotheses. Is it a lower-, upper-, or two-tailed test? ii. Let α = .05. What probability does α represent? 3. Assume σ = 0.30 and compute the test statistic.9. It is claimed by an advertisement that 4 out of 5 kids have energy gap. To test this, a random sample of 250 children were tested if they experienced this `energy gap.' It was found out that 202 of them is experiencing it. Which among the values below is the value of z? a. z ≈ 0.321 b. z ≈ 0.316 c. z ≈ -0.321 d. z ≈ -0.316
- A CI is desired for the true average stray-load loss ? (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with ? = 2.2. (Round your answers to two decimal places.) (a) Compute a 95% CI for ? when n = 25 and x = 53.7. , watts(b) Compute a 95% CI for ? when n = 100 and x = 53.7. , watts(c) Compute a 99% CI for ? when n = 100 and x = 53.7. , watts(d) Compute an 82% CI for ? when n = 100 and x = 53.7. , watts(e) How large must n be if the width of the 99% interval for ? is to be 1.0? (Round your answer up to the nearest whole number.)n = You may need to use the appropriate table in the Appendix of Tables to answer this question.3. If X has an exponential distribution with λ=2. Calculate the following The value of x such that P(X<x)=0.05 corresponds to x=?The following table gives the total endothermic reactions involving sodium bicarbonate Final Temperature Conditions Number of Reactions 266 K 13 271 K 60 274 K 92 Assume that reactions are independent. What is the mean of the number of reactions until the first final temperature is less than 272K? Report answer to 3 decimal places.
- 2 Given the exponential distribution: f(x) = {1/θ e^(-x/θ) ; x > 0 0; ew](a) Given that X is normally distributed with mean 10 and ?(? > 12) = 0.1587. What is the probability that X will fall in the interval (9, 11)? You are given: Φ(1) = 0.8413 and Φ(−1/2)=0.3085, where Φ(?) = ?(−∞ < ? < ?)such that ?~?(0,1). (b) Suppose that during rainy season on a tropical island the length of the shower has an exponential distribution, with parameter ? = 2, time being measured in minutes. What is the probability that a shower will last more than three minutes? If a shower has already lasted for 2 minutes, what is the probability that it will last for at least one more minute?Develop seasonal factors from the table below by following a 3-MA values for the time series data t 1 2 3 4 5 6 7 8 9 y 13 18 13 14 13 16 14 21 13
- A veterinary nutritionist developed a diet for overweight dogs. The total volume of food consumed remains the same, but one-half of the dog food is replaced with a low-calorie “filler” such as canned green beans. Six overweight dogs were randomly selected from her practice and were put on this program. Their initial weights were recorded, and they were weighed again after 4 weeks. The results of the experiment are shown below. At α=0.05, can it be concluded that the dogs significantly lost weight?(a) Determine the value of k for a valid pdf.(b) Complete the cdf of X .(c) What is the expected total deduction on a randomly chosen form?(d) Let Y = ln(X /5), where ln(·) is natural logarithm. Determine the pdf as wellas the cdf of Y , and further identify which common distribution that Y follows?A companies revenue is determined by R(n)=2^n(n^2+5). Where n is the number of months. What is the expected revenue after 6 months? 1 year? What is the change in revenue between months 4 and 7? What is the average change in revenue between the months 5 and 9?
