18. a simple random sample of size n is drawn from a population that is normally distributed. the sample mean, x, is found to be 50, and the sample standard deviation, s, is found to be 8. (a) construct a 98% confidence interval for m if the sample size, n, is 20. (b) construct a 98% confidence interval for m if the sample size, n, is 15. how does decreasing the sample size affect the margin of error, e? (c) construct a 95% confidence interval for m if the sample size, n, is 20. compare the results to those obtained in part (a). how does decreasing the level of confidence affect the margin of error, e? (d) could we have computed the confidence intervals in parts (a)–(c) if the population had not been normally distributed? why?

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

idk

step-by-step explanation:

true

step-by-step explanation:

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