he blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4

The approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.

Step-by-step explanation:

We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7.

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 = 247.3

            = standard deviation = 60.7

Now, according to the empirical rule;

Since it is stated that we have to calculate the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4, i.e;

         z-score for 65.2 =  

                                     =    = -3

         z-score for 429.4 =  

                                       =    = 3

So, it means that the approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.

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step-by-step explanation: