SITUATION 8 (a) The elongation of a steel bar under a particular load has been established to be normally distributed with mean of 0.05 inch and standard deviation of 0.01 inch. (a.1) Find the probability that the elongation of a steel bar is above 0.1 inch. (a.2) Find the probability that the elongation of a steel bar is between 0.025 and 0.065 inch.
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- From generation to generation, the average age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 37 smokers of this generation was done to see if the average starting age is at least 19. The sample average was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (c) O Part (d) State the distribution to use for the test. (Round your standard deviation to four decimal places.) O Part (e) What is the test statistic? (Round your answer to two decimal places.) --Select--- v = O Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. O If H, is false, then there is a chance equal…The heights of 5-year-old children are approximately normally distributed with average height of 100cm and standard deviation of 6cm. Using the emipiracal rule i am trying to figure out What percentage of 5-year-olds are between 90cm and 120cm?From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 41 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.2 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part 1) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value Part 2) Alpha (Enter an exact number as an integer, fraction, or decimal.)α = Part 3) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper…
- For each substance, estimate the standard deviation o by assuming uniform distribution and normal distribution shown in Table 8.11 in Section 8.8. (Round your answers to 4 decimal places.) Uniform Distribution Normal Distribution Chromium Barium FluorideFrom generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 42 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) State the distribution to use for the test. (Round your answers to four decimal places.) X ~ , What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) = What is the p-value? (Round your answer to four decimal places.)The length of eels (in cm) in a river may be assumed to be normally distributed with a mean of µ = 42 and a standard deviation of o = 6. An angler catches an eel from a river. Let: X = the length (in cm) of an eel a) If the normal length of eels is between 30 cm and 45 cm, what percentage of eels fall within this normal range? Round your answer to 2 decimal places. b) What is the probability that an eel is at least 51 cmin length? Round your answer to 4 decimal places. c) The middle 50% of the lengths (in cm) of the eels are between and Round your answers to 2 decimal places d) Due to the symmetry of the normal distribution we know that DIV 20 - DIV -
- From generation to generation, the average age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 37 smokers of this generation was done to see if the average starting age is at least 19. The sample average was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) + Part (a) + Part (b) + Part (c) A Part (d) State the distribution to use for the test. (Round your standard deviation to four decimal places.) X - N 19 2.1/37 E Part (e) O Part (f) O Part (g) O Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (1) Alpha: a =The variable W represents the weight of potatoes buns sold at the bakery. This variable is normally distributed with mean 90 g and standard deviation 6 g. (a) (i) Explain the meaning of S6 . (ii) Find the mean and standard deviation of S6 . (ii) Hence, Calculate P ( S6 2 560 g).The reading speed of second grade students in a large city is approximately normal, with a mean of 91words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).
- Suppose the mean cholesterol levels of women age 45-59 is 5.2 mmol/l and the standard deviation is 0.7 mmol/l. Assume that cholesterol levels are normally distributed. Find the probability that a woman age 45-59 has a cholesterol level above 6.1 mmol/l (considered a high level). Round to four decimal places.P(x > 6.1) = Suppose doctors decide to test the woman’s cholesterol level again and average the two values. Find the probability that this woman’s mean cholesterol level for the two tests is above 6.1 mmol/l. Round to four decimal places.P(x̄ > 6.1) = Suppose doctors being very conservative decide to test the woman’s cholesterol level a third time and average the three values. Find the probability that this woman’s mean cholesterol level for the three tests is above 6.1 mmol/l. Round to four decimal places.P(x̄ > 6.1) =14:45. (a) For a normal distribution with mean u and standard deviation o, obtain the first and third quärtiles and also the quartile deviation. (b) For a normal distribution with mean 50 and s.d. 15, find Q, and Q3. dial. aoSITUATION 6 (a) The elongation of a steel bar under a particular load has been established to be normally distributed with mean of 0.05 inch and standard deviation of 0.01 inch. (a.1) Find the probability that the elongation of a steel bar is below 0.15 inch. (a.2) Find the probability that the elongation of a steel bar is between 0.025 and 0.050 inch.