Question

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 249.9 and a standard deviation of 63.8. ​(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 122.3 and 377.5​?

b. What is the approximate percentage of women with platelet counts between 58.5 and 441.3​?

a. Approximately ____% of women in this group have platelet counts within 2 standard deviations of the​ mean, or between 122.3 and 377.5. ​(Type an integer or a decimal. Do not​ round.) b. Approximately nothing​% of women in this group have platelet counts between 58.5 and 441.3

(Type an integer or a decimal. Do not​ round.)

b. Approximately ______​%of women in this group have platelet counts between 58.5 and 441.3.

​(Type an integer or a decimal. Do not​ round.)

Answer 1

Answer:

Given that,

The blood platelet counts of a group of women have a​bell-shaped distribution with a mean of 249.9 and a standard deviation of 63.8.

(a).

The approximate percentage of women with platelet counts between 122.3 and 377.5 is:

First, compute the Z-score then find probability based on standard normal table.

For x=122.3 converts to

=-2.00

For x=377.5 converts to

=2.00

From the standard normal distribution table, the associated probability for Z values and subtract the probability is,

=0.9772-0.0228

=0.9544  95.44%

The approximate percentage of women with platelet counts between 122.3 and 377.5 is 95.44%.

(b).

The approximate percentage of women with platelet counts between 58.5 and 441.3 is:

First, compute the Z-score then find probability based on standard normal table.

For x=58.5 converts to

=-3.00

For x=441.3 converts to

=3.00

From the standard normal distribution table, the associated probability for Z values and subtract the probability is,

=0.9987-0.0013

=0.9974  99.74%

The approximate percentage of women with platelet counts between 122.3 and 377.5 is 99.74%