Arandom sample of size 100 is taken from a population with the mean as 76 and the variance as 256. what is probability of getting sample mean: a. between 74.4 and 78.4, b. less than 74.4, and c. greater than 78.4.

Given the population mean is and population standard deviation is .

Now sample mean is and standard deviation of the sample mean is .

Use Z-score for finding the probabilities. Use a standard normal distribution table.

a)The probability

b)The probability

c)The probability

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

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