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Westkost [7]
3 years ago
12

Solve for the indicated variable

Mathematics
1 answer:
GrogVix [38]3 years ago
7 0

Answer:

X_1=\frac{YX_2}{X_2-Y} \\\\

Step-by-step explanation:

\frac{1}{Y}=\frac{1}{X_1}+\frac{1}{X_2}

First subtract the 1/x2

\frac{1}{Y} - \frac{1}{X_2}=\frac{1}{X_1}

Next subtract the fractions on the left

\frac{X_2-Y}{YX_2}=\frac{1}{X_1}\\

Next Multiply by x1

\frac{(X_1)X_2-Y}{YX_2}=1\\

Next divide both sides by the remaining parts (not x1)

X_1=\frac{YX_2}{X_2-Y} \\\\

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Answer:

A) Approximate percentage of women with platelet counts within 2 standard deviations of the​ mean, or between 118.5 and 377.3 = 95%

B) approximate percentage of women with platelet counts between 53.8 and 442.0 = 99.7%

Step-by-step explanation:

We are given;

mean;μ = 247.9

standard deviation;σ = 64.7

A) We want to find the approximate percentage of women with platelet counts within 2 standard deviations of the​ mean, or between 118.5 and 377.3.

Now, from the image attached, we can see that from the empirical curve, the probability of 1 standard deviation from the mean is (34% + 34%) = 68 %.

While probability of 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%

Thus, approximate percentage of women with platelet counts within 2 standard deviations of the​ mean, or between 118.5 and 377.3 = 95%

B) Now, we want to find the approximate percentage of women with platelet counts between 53.8 and 442.0.

53.8 and 442.0 represents 3 standard deviations from the mean.

Let's confirm that.

Since mean;μ = 247.9

standard deviation;σ = 64.7 ;

μ = 247.9

σ = 64.7

μ + 3σ = 247.9 + 3(64.7) = 442

Also;

μ - 3σ = 247.9 - 3(64.7) = 53.8

Again from the empirical curve attached, we cans that at 3 standard deviations from the mean, we have a percentage probability of;

(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%

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