Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.118.11 and a standard deviation of 1.461.46. Using the empirical rule, what percentage of American women have shoe sizes that are at least 11.0311.03?

2.5% of American women have shoe sizes that are at least 11.03.

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 = 8.11

Standard deviation = 1.46

Using the empirical rule, what percentage of American women have shoe sizes that are at least 11.03?

11.03 = 8.11 + 2*1.46

So 11.03 is two standard deviations above the mean.

The empirical rule states that 95% of the measures are within 2 standard deviation of the mean. Since the distribution is symetric, of those 5% farther than two standard deviations of the mean, 2.5% are higher than 2 standard deviations above the mean and 2.5% are lower than 2 standard deviations below the mean.

So 2.5% of American women have shoe sizes that are at least 11.03.

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1