Question

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/mu​L.) 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​?

Answer 1

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

b)
`P(191.5<X<319.5)`

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

`z=(x-\mu)/(\sigma)`

And replacing we got:

`z=(191.5-255.4)/(63.9)= -1`

`z=(319.3-255.4)/(63.9)= 1`

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

Explanation:

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

`\mu = 255.4` represent the mean

`\sigma = 63.9` 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:

`P(191.5<X<319.5)`

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

`z=(x-\mu)/(\sigma)`

And replacing we got:

`z=(191.5-255.4)/(63.9)= -1`

`z=(319.3-255.4)/(63.9)= 1`

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