An underground military installation is fortified to the extent that it can withstand up to three
direct hits from air-to-surface missiles and still function. Suppose an enemy aircraft is armed
with missiles, each having a 30 % chance of scoring a direct hit.
i. What is the probability that the installation will be destroyed with the seventh missile fired
is obtained by fewer than nine air strikes?
ii. Find the expected air-to-surface missiles strike.
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 121.1-cm and a standard deviation of 2.2-cm. For shipment, 26 steel rods are bundled together.
Find P91, which is the average length separating the smallest 91% bundles from the largest 9% bundles.
P91 = -cm
Enter your answer as a number accurate to 2 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
A population of values has a normal distribution with μ=121.3 and σ=5.8. You intend to draw a random sample of size n=149.
Find the probability that a single randomly selected value is between 119.8 and 121.2.
P(119.8 < X < 121.2)
Find the probability that a sample of size n=149 is randomly selected with a mean between 119.8 and 121.2.
P(119.8 < M < 121.2)
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Brämhults Juice, based in Sweden, produces chilled fruit and vegetable juices. A manager at Brämhults is considering purchasing a new machine to bottle 16-fluid-ounce (473-milliliter) bottles of 100% pure carrot juice and wants an estimate of the differ- ence in the mean filling weights between the new machine and the old machine. Random samples of bottles of carrot juice that had been filled by both machines were obtained. Estimate the difference in the mean filling weights between the new and the old machines? Discuss the assumptions. Use a = 0.10.
Let p represent the proportion of the strawberries in a shipment that are bruised.
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article ''Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis'' (Intl. J. of Advanced Manuf. Tech., 2010: 117–134)). If
In simple terms, this mathematical branch will be familiar to students dealing with probability distribution and statistics as you seek answers to your random sample statistic equations. Take a look at the sampling distribution example that will make things clearer regardless of your subject. If you need additional help, consider sampling distribution examples with solutions that will have all the questions that will look alike to what you may have with your statistics regardless if there are sampling distribution problems or a complex sampling distribution equation. As always, start with sampling distribution questions first to identify the most efficient solution.