Uppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.2 and a standard deviation of 1.49. Using the empirical rule, what percentage of American women have shoe sizes that are less than 12.67

99.85% of American women have shoe sizes that are less than 12.67

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 8.2

Standard deviation = 1.49

Using the empirical rule, what percentage of American women have shoe sizes that are less than 12.67

12.67 = 8.2 + 3*1.49

12.67 is 3 standard deviations above the mean.

Since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above. Of those 50% above, 99.7% are between the mean and 12.67. So

0.5 + 0.997*0.5 = 0.9985

99.85% of American women have shoe sizes that are less than 12.67

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.

i can you with this sweetie!

step-by-step explanation: