The water flow rate through an 8-inch pipe is 1.600 gallons per minute. The water flow rate through a 4-inch pipe is 260 gallons
per minute. A 6-
inch pipe has a water flow rate at one half of the rate of an 8-inch pipe.
Part A
Write an equation to relate the flow of water from the 8-inch pipe, e, to the flow of water from the 4-inch pipe, 1. Enter your answer in simplest
torm
Part B
Winte an equation to relate the flow of water from the 6-inch pipe, s to the flow of water from the 8-inch pipe, e
S
inch pipe has a water flow rate at one half of the rate of an 8-inch pipe.
Part A
Write an equation to relate the flow of water from the 8-inch pipe, e, to the flow of water from the 4-inch pipe, 1. Enter your answer in simplest
torm
Part B
Winte an equation to relate the flow of water from the 6-inch pipe, s to the flow of water from the 8-inch pipe, e
S
2 answers:
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Answer:
(a) The distribution of the sample mean () is <em>N</em> (68, 4.74²).
(b) The value of is 0.7642.
(c) The value of is 0.3670.
Step-by-step explanation:
A random sample of size <em>n</em> = 10 is selected from a population.
Let the population be made up of the random variable <em>X</em>.
The mean and standard deviation of <em>X</em> are:
(a)
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Since the sample selected is not large, i.e. <em>n</em> = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.
Then, the mean of the distribution of the sample mean is given by,
And the standard deviation of the distribution of the sample mean is given by,
Thus, the distribution of the sample mean () is <em>N</em> (68, 4.74²).
(b)
Compute the value of as follows:
*Use a <em>z</em>-table for the probability.
Thus, the value of is 0.7642.
(c)
Compute the value of as follows:
Apply continuity correction as follows:
Thus, the value of is 0.3670.
