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- Continuous Distribution The quantity of aerated water that a machine puts in a bottle of a carbonated beverage follows normal distribution with a standard deviation of 0.25 g. At what “normal” (mean) weight should the machine be set so that no more than 8% of the bottles have more than 20 g of aerated water?Find the area of the shaded region. 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. 102 126 A symmetric bell-shaped curve is plotted over a horizontal scale. Two vertical lines run from the scale to the curve at labeled coordinates 102 and 126, which are both to the right of the curve’s center and peak. The area under the curve between the vertical lines is shaded. The area of the shaded region is enter your response here. (Round to four decimal places as needed.)Numbers are distributed average = 60 standard deviation = 5 a) Find the percentage of the distribution between the numbers x1 = 50 and x2 = 65.b) What should be the boundaries that determine 75% of the distribution in the center.
- 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.)Measuring lung function: One of the measurements used to determine the health of a person's lungs is the amount of air a person can exhale under force in one second. This is called forced expiratory volume in one second, and is abbreviated FEV1. Assume the mean FEV1 for 10-year-old boys is 2.1 liters and that the population standard deviation is =σ0.5 . A random sample of 7010-year-old boys who live in a community with high levels of ozone pollution are found to have a sample mean FEV1 of 2.03 liters. Can you conclude that the mean FEV1 in the high-pollution community is less than 2.1 liters? Use the =α0.05 level of significance and the P-value method with the TI-84 calculator.IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X=X= IQ of an individual.(a) Find the z-score for an IQ of 106, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 106. (c) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place). Shade: . Click and drag the arrows to adjust the values. -1.5
- Screw lengths produced by automatic machines producing uniform screws; Normal distribution with a mean of 3.0 cm and a standard deviation of 0.009 cm. Screws with lengths shorter than 2.98cm and those longer than 3.02cm are not used because they are defective. Few% of the screws produced on this machine are defectiveMeasuring lung function: One of the measurements used to determine the health of a person's lungs is the amount of air a person can exhale under force in one second. This is called forced expiratory volume in one second, and is abbreviated FEV1. Assume the mean FEV1 for 10 -year-old boys is 2.1 liters and that the population standard deviation is =σ0.4 . A random sample of 35 10 -year-old boys who live in a community with high levels of ozone pollution are found to have a sample mean FEV1 of 1.98 liters. Can you conclude that the mean FEV1 in the high-pollution community differs from 2.1 liters? Use the =α0.10 level of significance and the P -value method with the TI-84 calculator. Part: 0 / 4 0 of 4 Parts Complete Part 1 of 4 State the appropriate null and alternate hypotheses. :H0 :H1 This hypothesis test is a ▼(Choose one) test.The tolerance limits for a particular quality characteristic (e.g., length, weight, or strength) of a particular product are the minimum and/or maximum values at which the product will operate properly. Tolerance limits are set by the engineering design function of the manufacturing operation. The tensile strength of a particular metal part can be characterized as being normally distributed with a mean of 25 pounds and a standard deviation of 2 pounds. The upper and lower tolerance limits for the part are 30 pounds and 21 pounds respectively. A part that falls within the tolerance limits results in a profit of $10. A part that falls below the lower tolerance limit costs the company $2; a part that falls above the upper tolerance limit costs the company $1. Find the company’s expected profit per metal part produced.
- 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 0.9 A graph with a bell-shaped curve, divided into 2 regions by a line from top to bottom, on the right side. The region left of the line is shaded and labeled 0.9. The x-axis below the line is labeled "x". The indicated IQ score, x, is(Round to one decimal place as needed.)The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for 3 years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will break down during the guarantee period. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability. P(0 < x < ____________) = ___________ (Use zero for the minimum value of x.)Weights of a certain product follow Normal Distribution with unknownparameters. Based on the past experience, we knew that 7.5% of all theproducts weigh less than 11.188 gr and 6% of all products weigh more than18.0765 gr. Subject to the experience, calculate parameter values of thedistribution.