In: Statistics and Probability
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/muL.) 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:
Given that,
The blood platelet counts of a group of women have abell-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%