A water tank is leaking water at a rate of 300 gallons per minute. What is this rate in gallons per second
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Answer:
The sample size should be at least 79.
Step-by-step explanation:
Let Y be be the resting glocose level of a member of the population chosen randomly, then Y is a random variable with unkown mean λ and Standard deviation σ = 27.
Let X be the sample mean of a sample of lenght n. X has the same mean as Y and the standard deviation is
If n is reasonable high, the Central Limit Theorem states that X has distribution approximately Normal, with mean λ and Standard deviation
If we standarize X, we get a random variable W
The values of W are tabulated and can be found on the attached file. We want a 95% confidence interval, so we want Z such that
P(-Z < w < Z) = 0.95
Using the symmetry of the normal density function, we get that
P(W < Z) = 0.975
If we look at the table, we will find that Z = 1.96, therefore we have
Equivalently,
Taking out the X and the sign, after reverting the inequalities, we obtain
Thus, a confidence interval with 95% confidence is
The (absolute) margin of error of this interval is we want that number to be at most 5, so we take n such that
We take n = 79. I hope that works for you!
A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The amount of paint needed to paint 20 pillars is 9.874 gallons.
<h3>What is a cylinder?</h3>A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.
The curved surface area of a single-cylinder with a diameter of 2.5 feet and a height of 22 feet will be,
Curved surface area = πDh = π × 2.5 × 22 = 172.7875 ft²
The total area of 20 pillar = 20 × 172.7875 ft² = 3,455.75191 ft²
Since a gallon of paint can cover only 350 ft², therefore, the amount of paint that will be needed to paint 3,455.75191 ft² can be written as,
Hence, the amount of paint needed to paint 20 pillars is 9.874 gallons.
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