The water content of soil from a borrow site is normally distributed with a mean of μ = 14.2% and standard deviation of a = 2.3%. What is the probability that a sample taken from the site will have a water content above 16% or below 12%?
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- Speeds of cars in an expressway are monitored by high-speed camera units. The minimum speed of cars in the expressway is 60 kph and the maximum speed is 100 kph. Cars going below the minimum, or going above the maximum, are apprehended. Suppose that speed of the cars on the expressway are normally distributed with a mean of 75kph and a standard deviation of 10 kph. What percentage of the cars travelling on the expressway will not be apprehended? Note: Write your answer as percentage with two decimal places (i.e. 87.26%).The lifetime of a particular component is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. What is the 80th percentile of component lifetimes?Diameters of bolts produced by a particular machine are normally distributed with mean 0.760 cm and standard deviation 0.012 cm. Specifications call for diameters from 0.730 cm to 0.780 cm. What percentage of bolts will meet these specifications?
- A manufacturing process produces a critical part of the average length 110 millimeters, with a standard deviation of 2 millimeters. All parts deviating by more than 5 millimeters from the mean must be rejected. What percentage of the parts must be rejected, on average? Assume a normal distribution.According to National Health Survey heights of men are normally distributed with mean of μ=69.0 inches and standard deviation σ=2.50 . What length of a bed is satisfactory for at least 95% of all men?Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.3 and the sample standard deviation was 1.4. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.) State the appropriate hypotheses. ⒸH₂: μ = 48 Ha: > 48 Ho:μ = 48 H₂H 48 H₂: μ = 48 Ho: μ< 48 H₂₁:μ = 48 USE SALT Ho: M = 48 H₂:48 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t= 7.68 X P-value =
- Type I error: Washers used in a certain application are supposed to have a thickness of 2 millimeters. A quality control engineer measures the thicknesses for a sample of washers and tests H0: μ = 2 versus H1: μ ≠ 2. a. If a Type I error is made, what conclusion will be drawn regarding the mean washer thickness?Molybdenum rods are produced by a production line setup. It is desirable to check whether the process is in control, i.e. equal to 2.2 inches. Let X = length of such a rod. Assume X is approximately normally distributed where the mean and variance are unknown. Take n = 400 sample rods, with sample average length 2 inches with a standard deviation of 0.5 inches. Using α=0.05, find the test statistic of the necessary test to be held and the corresponding critical value?Bolts produced by a machine are acceptable provided that the length is within the range from 5.95 to 6.05 centimeters. Suppose that the bolts produced by the machine are normally distributed with a mean of 6 cm with a standard deviation of 0.02 cm. What percentage of bolts produced by the machine will be acceptable?
- The time needed to find a parking space is normally distributed with a mean of 20 minutes and a standard deviation of 5.18 minutes. 90% of the time, it takes less than how many minutes to find a parking space?assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation of 0.070 g. A vending machine will only accept coins weighing between 5.48 and 5.82 g. what is the percentage of legal quarters that will be rejected?