The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 255.4 and a standard deviation of 63.9. (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 3 standard deviations of the mean, or between 63.7 and 447.1? b. What is the approximate percentage of women with platelet counts between 191.5 and 319.3?

a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data

b)

We can find the number of deviations from the mean for the limits using the z score formula given by:

And replacing we got:

So we have values within 1 deviation from the mean and using the empirical rule we know that we have 68% of the values for this case

Step-by-step explanation:

For this case we have the following properties for the random variable of interest "blood platelet counts"

represent the mean

represent the population deviation

Part a

From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data

Part b

We want this probability:

We can find the number of deviations from the mean for the limits using the z score formula given by:

And replacing we got:

So we have values within 1 deviation from the mean and using the empirical rule we know that we have 68% of the values for this case

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

step-by-step explanation:

infinity is the answer