Dr. Patton is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a population standard deviation of 2.44 words per essay. For her 10 a. m. section of 40 students, the mean number of misspelled words was 6.05. Construct a 95% confidence interval for the mean num- ber of misspelled words in the population of student essays.

The confidence interval is (5.2938, 6.8062)

Step-by-step explanation:

Given that:

Standard deviation (σ) = 2.44 words per essay,

Mean (μ) = 6.05,

Confidence interval (c) = 95% = 0.95.

number of students (n) = 40 students

α = 1 - c = 1 - 0.95 = 0.05

From the probability table,

The margin of error (e) is given by the equation:

Substituting values:

The confidence interval  is given by (μ - e, μ + e).

Therefore: The confidence interval = (μ - e, μ + e)  = (6.05 - 0.7562, 6.05 + 0.7562) = (5.2938, 6.8062)

The confidence interval is (5.2938, 6.8062)

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.