Practice with
Normal Distribution and Standard Deviation
Topic Index | Algebra2/Trig Index | Regents Exam Prep Center


Solve the following problems involving normal distributions and standard deviation.
If the question presents a situation that can be solved using increments of one-half
of one standard deviation, use the chart (below).  If not, use your graphing calculator.

 

1. The amount of mustard dispensed from a machine at The Hotdog Emporium is normally distributed with a mean of 0.9 ounce and a standard deviation of 0.1 ounce.  If the machine is used 500 times, approximately how many times will it be expected to dispense 1 or more ounces of mustard.

Choose:

5            16                  80               100


Answer

 

 

2. Professor Halen has 184 students in his college mathematics lecture class.  The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9.  How many students in the class can be expected to receive a score between 82 and 90?  Express answer to the nearest student.
  


Answer

 

 

3. A machine is used to fill soda bottles.  The amount of soda dispensed into each bottle varies slightly.  Suppose the amount of soda dispensed into the bottles is normally distributed.  If at least 99% of the bottles must have between 585 and 595 milliliters of soda, find the greatest standard deviation, to the nearest hundredth, that can be allowed.


Answer

 

 

4.  Residents of upstate New York are accustomed to large amounts of snow with snowfalls often exceeding 6 inches in one day.  In one city, such snowfalls were recorded for two seasons and are as follows (in inches):

8.6, 9.5, 14.1, 11.5, 7.0, 8.4, 9.0, 6.7, 21.5, 7.7, 6.8, 6.1, 8.5, 14.4, 6.1, 8.0, 9.2, 7.1

What are the mean and the population standard deviation for this data, to the nearest hundredth?
  


Answer

 

 

5. Neesha's scores in Chemistry this semester were rather inconsistent:  100, 85, 55, 95, 75, 100. 

For this population, how many scores are within one standard deviation of the mean?

    


  Answer

 

 

6.  Battery lifetime is normally distributed for large samples.  The mean lifetime is 500 days and the standard deviation is 61 days.  To the nearest percent, what percent of batteries have lifetimes longer than 561 days?

  


Answer



 

7. The number of children of each of the first 41 United States presidents is given in the accompanying table.  For this population, determine the mean and the standard deviation to the nearest tenth.

How many of these presidents fall within one standard deviation of the mean?


Answer


 

 

 

8.  From 1984 to 1995, the winning scores for a golf tournament were 276, 279, 279, 277, 278, 278, 280, 282, 285, 272, 279, and 278.  Using the standard deviation for this sample, Sx, find the percent of these winning scores that fall within one standard deviation of the mean. 

     


Answer

 

 

9.  A shoe manufacturer collected data regarding men's shoe sizes and found that the distribution of sizes exactly fits the normal curve.  If the mean shoe size is 11 and the standard deviation is 1.5, find:
a.  the probability that a man's shoe size is greater than or equal to 11.

b.  the probability that a man's shoe size is greater than or equal to 12.5.

c.       


Answer

 


 
10.  Five hundred values are normally distributed with a mean of 125 and a standard deviation of 10.
a.  What percent of the values lies in the interval 115 - 135,
     to the nearest percent?
b.  What percent of the values is in the interval 100 - 150,
     to the nearest percent?
c.  What interval about the mean includes 95% of the data?
d.  What interval about the mean includes 50% of the data?
 


Answer


 

 
11.  A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years.  The ages are normally distributed.  How many students are younger than 16.2 years?  Express answer to the nearest student?


Answer