AP Statistics
Practice- Normal Distributions and CLT
Name:____________________________________
Date:_____________________________________
1.
In a standard normal distribution, find P(.25  z  2)
2.
Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5. Find:
a)
the probability that a value is between 65 and 80, inclusive.
b)
the probability that a value is greater than or equal to 75.
c)
the probability that a value is less than 62.
d)
the 90th percentile for this distribution.
3.
The lifetime of a battery is normally distributed with a mean life of 40 hours and a standard deviation of
1.2 hours. Find the probability that a randomly selected battery lasts longer than 42 hours.
4.
Bill claims that he can do more push-ups than 90% of the boys in his school. Last year, the average boy
did 50 push-ups, with a standard deviation of 10 pushups. Assume push-up performance is normally
distributed. How many pushups would Bill have to do to beat 90% of the other boys?
5.
The Acme Light Bulb Company has found that an average light bulb lasts 1000 hours with a standard
deviation of 100 hours. Assume that bulb life is normally distributed. What is the probability that a
randomly selected light bulb will burn out in 1200 hours or less?
6.
Graduate Management Aptitude Test (GMAT) scores are widely used by graduate schools of business as
an entrance requirement. Suppose that in one particular year, the mean score for the GMAT was 476,
with a standard deviation of 107. Assuming that the GMAT scores are normally distributed, answer the
following questions:
7.
a.
What is the probability that a randomly selected score from this GMAT falls between 476 &
650?
b.
What is the probability of receiving a score greater than 750 on this GMAT.
For women aged 18-24 systolic blood pressure (in mm Hg) is normally distributed with a mean of 114.8
and a standard deviation of 13.1 (based on data from the National Health Survey). Hypertension is
commonly defined as a systolic blood pressure above 140. Use the Central Limit Theorem to find the
following:
a.
If a woman between the ages of 18 and 24 is randomly selected, find the probability her systolic
blood pressure is greater than 140.
b.
If 4 women in that age bracket are randomly selected, find the probability that their mean
systolic blood pressure is greater than 140.
c.
If 16 women in that age bracket are randomly selected, find the robability that their mean
systolic blood pressure is greater than 100 and less than 120.
d.
If a physician is given a report stating that 4 women have a mean systolic blood pressure below
140, can she conclude that none of the women have hypertension (blood pressure greater than
140)?
AP Statistics
Answer Key
Name:____________________________________
Date:_____________________________________
1.
normalcdf( -0.25, 2, 0, 1) = 0.576
2.
a.
b.
c.
d.
3.
normalcdf( 42, 1000000000, 40, 1.2) = 0.0478
4.
invnorm (0.90, 50, 10) = 62.816
5.
normalcdf( 0, 1200, 1000, 100) = 0.977
**Note: we start with 0 here because you can’t have less than 0 hours of light bulb life
6.
a.
b.
normalcdf( 476, 650, 476, 107) = 0.448
normalcdf( 750, 800 , 476, 107) = 0.00399
**Note: max score on the GMAT is 800
7.
a.
normalcdf( 140, 1000000000, 114.8, 13.1) = 0.0272
13.1 

normalcdf 140, 1000000000, 114.8,
 = 0.0000597
4 

b.
c.
d.
normalcdf( 65, 80, 70, 4.5) = 0.854
normalcdf( 75, 1000000000, 70, 4.5) = 0.133
normalcdf( -1000000000, 62, 70, 4.5) = 0.0377
invnorm( 0.90, 70, 4.5) = 75.767

13.1 
normalcdf 100, 120, 114.8,
 = 0.944
16 

13.1 

normalcdf  0, 140, 114.8,
 = 0.99994
4 

In this case, the probability that an average group of four women selected at random will have
an average systolic blood pressure below 140 is almost 100%. It is almost a certainty.
Therefore, if a doctor received a report stating that a particular group of four women have an
average systolic blood pressure below 140 she can conclude that none of them have
hypertension.