What 2 numbers multiply to 30 and add to -11
1 answer:
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There are ways for the teacher to decide which student she will teach during each lesson time if she must teach each student exactly 3 times. Here, "!" represents the factorial.
A number's factorial is the result of multiplying the integer by each natural number below it. Factorial can be symbolized by the letter "!". Thus, n factorial is denoted by n! and is the result of the first n natural numbers.
A whole number's "n" factororial is the sum of that number and each whole number up to one.
When a question asks you to determine how many different ways you can arrange or order a given number of items, you use a factorial.
Learn more about factorials here:
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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.