Question

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 253.8 and a standard deviation of 60.5. ​(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 2 standard deviations of the​ mean, or between 132.8 and 374.8​?

b. What is the approximate percentage of women with platelet counts between 193.3 and 314.3​?

Answer 1

Answer
(A) We know that according to empirical rule, 95% of the data lies between 2 standard deviation from the mean

So, there will be approximately 95% of data within the range of 132.8 and 374.8

(B) We can write

193.3 as 253.8-60.5, i.e. one standard deviation below the mean

and

314.3 as 253.8 + 60.5, i.e. one standard deviation above the mean

According to empirical rule,

we know that 68% of data values lie within 1 standard deviation from the mean

So, there will be approximately 68% of data within the range of 193.3 and 314.3