Using the accompanying table of data, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.5 (All units are 1000 cells/muμL.) Using Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within 3 standard deviationsdeviations of the mean?
What are the minimum and maximum possible platelet counts that are within 3 standard deviationsdeviations of the mean?
Using Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within 3 standard deviations of the mean?
At least ? of women have platelet counts within 3 standard deviations of the mean. (Round to the nearest integer asneeded.)
The minimum posssible platelet count within 3 standard deviations of the mean is ? . The maximum possible platelet count within 3 standard deviations of the mean is ?

Question

09-05-2020
Mathematics

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Using the accompanying table of data, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.5 (All units are 1000 cells/muμL.) Using Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within 3 standard deviationsdeviations of the mean?
What are the minimum and maximum possible platelet counts that are within 3 standard deviationsdeviations of the mean?
Using Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within 3 standard deviations of the mean?
At least ? of women have platelet counts within 3 standard deviations of the mean. (Round to the nearest integer asneeded.)
The minimum posssible platelet count within 3 standard deviations of the mean is ? . The maximum possible platelet count within 3 standard deviations of the mean is ?

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joaobezerra joaobezerra · Answer 1 · 2020-05-12T02:21:19+02:00

Answer:

At least 89% of women have platelet counts that are within 3 standard deviations of the mean.

The minimum possible platelet count that is within 3 standard deviations of the mean is 58.6 and the maximum is 451.6.

Step-by-step explanation:

The Chebyshev Theorem states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 255.1

Standard deviation = 65.5

Using Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within 3 standard deviations of the mean?

At least 89% of women have platelet counts that are within 3 standard deviations of the mean.

What are the minimum and maximum possible platelet counts that are within 3 standard deviations of the mean?

Minimum: 255.1 - 3*65.5 = 58.6

Maximum: 255.1 + 3*65.5 = 451.6

The minimum possible platelet count that is within 3 standard deviations of the mean is 58.6 and the maximum is 451.6.

psm22415 psm22415 · Answer 2 · 2021-12-06T17:02:23+01:00

The minimum possible platelet count that is within 3 standard deviations of the mean is 58.6 and the maximum is 451.6.

Given that,

Blood platelet counts of women have a bell-shaped distribution with a mean of 255.1,

And a standard deviation of 65.5 (All units are 1000 cells/muμL.)

Using Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within 3 standard deviations of the mean.

We have to determine,

What are the minimum and maximum possible platelet counts that are within 3 standard.

According to the question,

Chebyshev's Theorem estimates the minimum proportion of observations that fall within a specified number of standard deviations from the mean.

This theorem applies to a broad range of probability distributions. Chebyshev's Theorem is also known as Chebyshev's Inequality.

C = 255.1

Standard deviation = 65.5

At least 89% of women have platelet counts that are within 3 standard deviations of the mean.

[tex]Minimum: 255\times 1 - 3\times65.5 = 255.1-196.5 = 58.6\\\\Maximum: 255\times 1 + 3\times65.5 = 255 + 196.5 =451.6[/tex]

Hence, The minimum possible platelet count that is within 3 standard deviations of the mean is 58.6 and the maximum is 451.6.

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