Chapter 6 Discussion

Sample Problem with calculation and notation shown; (This problem finds the probability of one randomly chosen woman from the population of all women and does not use Central Limit Theorem)::

Pulse rates of adult women are normally distributed with a mean of 74 beats per minute and a standard deviation of 12.5 beats per minute.

Question:  If one adult woman is randomly selected from the population of all adult women, what is the probability her heart rate is greater than 80.25 bpm?

Answer:

First find the number of standard deviations 80.25 bpm is from the mean:  z=80.25−7412.5=0.50       

Then find the probability x is greater than 80.25 bpm which is the probability z is greater than 0.50:  P(x > 80.25) = P(z > 0.50) = 1 – 0.6915 = .3085.  

The following problem uses Central Limit Theorem (finding the probability that the mean of one random group from all possible groups of the same size from the population):

Use this information to complete questions at numbers 1-4 below:  Pulse rates of adult women are normally distributed with a mean of 74 beats per minute and a standard deviation of 12.5 beats per minute. 

1. If 16 women are randomly selected from all possible groups of 16 women in the population, what is the probability their mean heart rate is greater than 80.25 bpm? *Note – when finding the number of standard deviations x-bar is from the mean, be sure to use the correct formula for z – divide by sigma of x-bar rather than sigma.

First: Show the formula to find the number of standard deviations x-bar is from the mean:   z =

Second: Show the probability notation to find:  P(x¯>80.25)=

1. Why do we use  P(x-bar)  instead of P(x) when finding a probability using Central Limit Theorem?
2. Why is the value for the standard deviation of the sampling distribution different than the value of the population standard deviation when Central Limit Theorem is used? (Study textbook page 279)
3. Why can we use Central Limit Theorem even though the sample size is less than 30?

"96% of our customers have reported a 90% and above score. You might want to place an order with us."