Question

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/muμ​L.) 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 as​needed.)
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 ?

Answer 1

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.