The blood platelet counts of a group of women have a bell-shaped distribution with a mean of and a standard deviation of . (All units are 1000 cells/L.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within standard of the mean, or between and ?
b. What is the approximate percentage of women with platelet counts between and ?

(a) Approximately 95% of women with platelet counts within 2 standard deviations of the mean.

(b) Approximately 99.7% of women have platelet counts between 65.2 and 431.8.

Step-by-step explanation:

The complete question is: The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1. (All units are 1000 cells/mul.) using the empirical rule, find each approximate percentage below.

a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 126.3 and 370.7?

b. What is the approximate percentage of women with platelet counts between 65.2 and 431.8?

We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1.

Let X = the blood platelet counts of a group of women

The z-score probability distribution for the normal distribution is given by;

                             Z  =    ~ N(0,1)

where, = population mean = 248.5

            = standard deviation = 61.1

Now, the empirical rule states that;

(a) The approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 126.3 and 370.7 is given by;

As we know that;

P( < X < ) = 0.95

P(248.5 - 2(61.1) < X < 248.5 + 2(61.1)) = 0.95

P(126.3 < X < 370.7) = 0.95

Hence, approximately 95% of women with platelet counts within 2 standard deviations of the mean.

(b) The approximate percentage of women with platelet counts between 65.2 and 431.8 is given by;

Firstly, we will calculate the z-scores for both the counts;

z-score for 65.2 =

                           = = -3

z-score for 431.8 =

                           = = 3

This means that approximately 99.7% of women have platelet counts between 65.2 and 431.8.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)