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- Estimate the age of a newly discovered fossil for which the ratio of carbon-14 to carbon-12 is R=1/1014.The variable X, is the carbon monoxide concentration in air, and ten measurements are obtained as follows: 10.25, 10.37, 10.66, 10.47, 10.56, 10.22, 10.44, 10.38, 10.63, 10.40 mg/m3 . (i) Test whether the mean concentration of carbon monoxide in air is 10.00 mg/m3 . (ii) Calculate the power of the above test if the mean concentration of carbon monoxide in the alternative hypothesis is assumed to be 10.75mg/m3 .The acceptable level for insect filth in a certain food item is 5 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of x = 5.3 insect fragments per ten-gram portion. Complete parts (a) through (c) below. H = 5 (Round to three decimal places as needed.). o: = 0.316 (Round to three decimal places as needed.) (c) What is the probability a simple random sample of 50 ten-gram portions of the food item results in a mean of at least 5.3 insect fragments? P(x2 5.3) = (Round to four decimal places as needed.)
- The acceptable level for insect filth in a certain food item is 5 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of x = 5.3 insect fragments per ten-gram portion. Complete parts (a) through (c) below. o: = 0.316 (Round to three decimal places as needed.) (c) What is the probability a simple random sample of 50 ten-gram portions of the food item results in a mean of at least 5.3 insect fragments? P(x 2 5.3) = ||| (Round to four decimal places as needed.)Suppose fox)= x is to be approximated near x 8. Find the linear approximation to fat x= 8. Then, complete the following table, showing the errors in the various approximations. Use a calculator to obtain the exact values. The percent error is calculated using the formula below. Comment on the 8.1 8.01 8.001 8.0001 7.9999 7.999 7.99 7.9 Linear Exact Percent арprox. value error behavior of the errors as x approaches 8. 100 lapproximation - exact lexact Complete the linear approximation column of the table. (Round to seven decimal places as needed.) Linear approx 8.1 8.01 8.001 8.0001 7.9999 7.999 7.99 7.9The average concentration of cadmium (Cd) in tea leaves sample is 68.0(±1.5) ppm Cd. Calculate .8 * the coefficient of variation (CV) for sample is 2.2 O 0.11 O 0.012 O 3.4 O 0.012 O
- b. 1 1.5 2.5 3 h(q) 110 366 1215 4034 13394 Estimate h'(2) using the table above. h'(2) 2Let X denote the final depth of a crack on a railway, X~ N(5.496mm, 0.0672 mm²). What values of the final crack depth would be exceeded by only 5% of all cracks?The mean and standard deviation of a normal variate are 70 and 16 respectively. Find P(38 < x < 46). If P(0 < z < 1.88) = 0.19699, the area under the standard curve which %3D is the left of z = 1.88 is . A mean and standard deviation of a normal variate are 8 and 4 respectively. Find P(5 < x < 10)
- la). The null hypothesis is that the difference in the grams of sugar between ultra-processed and processed food μ = 0 (Ho: μ = 0). Write an example alternative hypothesis for the mean (µ) difference between ultra-processed foods (up) and processed foods (μ). 1b). Next, generate 1,000 samples. Let's say that you asked students in our class to calculate the difference in the amount of sugar between their ultra-processed food and processed food at home, which had a mean (u) sugar difference of 14.75 grams of sugar. Do you have evidence to reject the null hypothesis? 1c). Let's say that your sample difference in the amount of sugar between ultra-processed food and processed food at home was 4.75 grams of sugar. Do you have evidence to reject the null hypothesis? 1d). What is a 92% confidence interval for the data? Please write it using the full confidence interval interpretation language (e.g., I am 92% confident that...). le). What percent of the data lie to the left of -14.25 grams of…Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. x 0.2525 A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the scale to the curve at labeled coordinate x, which is to the right of the curve’s center and peak. The area under the curve to the right of the vertical line is shaded and labeled 0.2525. Question content area bottom Part 1 The indicated IQ score is enter your response here. (Round to the nearest whole number as needed.)I. Solve for Z and find its area 1. Mean = 81, score: x = 71.5, standard deviation: o = 9. 2. Mean = 47, score: x = 55.6, standard deviation: o = 4. 3. Mean = 68, score: x = 78.8, standard deviation: o = 6. 4. Mean = 51, score: x = 69, standard deviation: o =7. 5. Mean = 85, score: x = 93, standard deviation: o =5. 6. The mean expenses of Dela Cruz Family is PhP12,600 every 15 days and the standard deviation is PhP 1, 570., If the expenses are normally distributed, what is the probability of consuming less than PhP 11,000 in 15 days? 7. The mean production of factory workers is 10 finished products per hour, with a standard deviation of 1.5 products/hour. What is the probability of finishing: a. less than 12.8 products/hour? b. more than 12 products/hour? 8. The mean weight of insects for laboratory experiments is 13.2 g, with the standard deviation of 0.8 g. What is the probability of randomly selecting insects with weight of: a. 14 g? b. 13.1 to 13.6 g? 9. The lifetime of CP…