MATHEMATICS MIDDLE SCHOOL

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.42 and a standard deviation of 1.52. Using the empirical rule, what percentage of American women have shoe sizes that are greater than 9.94? Please do not round your answer.

Answers

Answer 1

Answer:

Answer:

The percentage of the women have size shoes that are greater than

9.94 is 16%

Step-by-step explanation:

* Lets revise the empirical rule

- The Empirical Rule states that almost all data lies within 3 standard

deviations of the mean for a normal distribution.

- 68% of the data falls within one standard deviation.

- 95% of the data lies within two standard deviations.

- 99.7% of the data lies Within three standard deviations

* The empirical rule shows that

# 68% falls within the first standard deviation (µ ± σ)

# 95% within the first two standard deviations (µ ± 2σ)

# 99.7% within the first three standard deviations (µ ± 3σ).

* Lets solve the problem

- The shoe sizes of American women have a bell-shaped distribution

with a mean of 8.42 and a standard deviation of 1.52

∴ μ = 8.42

- The standard deviation is 1.52

∴ σ = 1.52

- One standard deviation (µ ± σ):

∵ (8.42 - 1.52) = 6.9

∵ (8.42 + 1.52) = 9.94

- Two standard deviations (µ ± 2σ):

∵ (8.42 - 2×1.52) = (8.42 - 3.04) = 5.38

∵ (8.42 + 2×1.52) = (8.42 + 3.04) = 11.46

- Three standard deviations (µ ± 3σ):

∵ (8.42 - 3×1.52) = (8.42 - 4.56) = 3.86

∵ (8.42 + 3×1.52) = (8.42 + 4.56) = 12.98

- We need to find the percent of American women have shoe sizes

that are greater than 9.94

∵ The empirical rule shows that 68% of the distribution lies

within one standard deviation in this case, from 6.9 to 9.94

∵ We need the percentage of greater than 9.94

- That means we need the area under the cure which represents more

than one standard deviation (more than 68%)

∵ The total area of the curve is 100% and the area within one standard

deviation is 68%

∴ The area greater than one standard deviation = (100 - 68)/2 = 16

∴ The percentage of the women have size shoes that are greater

than 9.94 is 16%

Answer 2

Answer:

Final answer:

Less than 5% of American women have shoe sizes greater than 9.94.

Explanation:

The empirical rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and more than 99% falls within three standard deviations of the mean.

In this case, the mean shoe size for American women is 8.42 and the standard deviation is 1.52. To calculate the percentage of American women with shoe sizes greater than 9.94, we need to find the proportion of the data that falls above this value.

First, we calculate the number of standard deviations that 9.94 is away from the mean: (9.94 - 8.42) / 1.52 = 0.9895 standard deviations.

Based on the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Since 9.94 is less than two standard deviations away from the mean, we can estimate that less than 5% of American women have shoe sizes greater than 9.94. Therefore, the percentage of American women with shoe sizes greater than 9.94 is less than 5%.

Learn more about Percentage here:

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Answers

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a trail mix recipe calls for 1/3 pound of mixed nuts, 4/15 pound of raisins and 2/5 pounds of granola. What is the ratio of raisins to mixed nuts in simplest form?

Answers

The unsimplified ratio of raisins to mixed nuts in the trail mix is:

4/15 to 1/3

To simplify this, it is easiest to make 1/3 into an equivalent fraction with the denominator 15 by multiplying both the numerator and the denominator by 5.

1 * 5 / 3 * 5 = 5 / 15

If we substitute in this new value, our ratio is:

4/15 : 5/15

Because both of these fractions have the same denominators, we can just compare their numerators, so we can simplify our ratio to be:

4:5

Therefore, your final answer is a 4:5 ratio of raisins to mixed nuts.

Hope this helps!

Answer

$\text {the ratio of raisins to mixed nuts is}$ ${\boxed {4:5}}$

The problem is asking us to determine thew ratio of raisins to mixed nuts in the simplest form.

Solution & detailed explanation

Let's start.

We have two fractions here.

$(1)/(3) \text{and} (4)/(15)$

We would need to simplify both of the fractions, the LCM of both fractions is 15.

$(1)/(3) \rightarrow (5)/(15)$

Since we now have the same denominators we could convert this into a ratio.

4:5

Therefore, the ratio of of raisins to mixed nuts is 4:5

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