Normal Distribution

  

NOTE: THE CURVES AND AREAS THAT FOLLOW ARE NOT DRAWN TO SCALE

  

#

Problem 

Notes 

POINT VALUE

YOUR ANSWER(S)

 

1

DELETED

 

2

In figure b-2, if the right tail = 16.6%,   how much area

     (probability) is in the non-tail ?

4 place decimal

Like 0.2563

                    B-2

3

 

3

DELETED

 

4

In figure b-2, if the large area   (probability) = 77.1%, how much area is in the right tail ?

2 place %

3

 

5

DELETED

 

6

If a z score is found to be 0.78, what   is the resulting probability (AREA) TO THE LEFT OF THE Z SCORE ? 

4 place decimal

Like 0.7563

3

 

7

 If a probability or area is found to   be 0.7190, what is the z score ? 

2 place decimal like 0.77 or 1.35

  

3

 

8

 If a probability or area is found to   be 0.3399, what is the z score ? 

2 place decimal like 0.77 or - 1.09

  

3

 

9

If a probability or area is found to   be 0.7370, what is the z score ? USE THE FIGURE FOR #7 ABOVE

2 place decimal like 0.77 or 2.59

3

 

10

If a z score is found to be -2.56 , what is the resulting probability   ? USE THE FIGURE FOR #8 

4 place decimal

Like 0.2563

3

 

11

If a z score is found to be – 1.0 , what is the resulting probability   ? 

4 place decimal

Like 0.2563

USE THE FIGURE FOR # 8

3

 

12

If a probability or area is found to be 0.0283, what is the z score ?   

2 place decimal like 0.77

USE FIGURE FOR #8

3

 

13

If a probability or area is found to be 0.5697, what is the z score ?   

2 place decimal like 0.77

USE #7 FIGURE

3

PART 2

  

#

Problem 

Notes 

POINT VALUE

YOUR ANSWER(S)

 

1

Find the area ( probability ) to the   left of a z score of 2.16

Round to 4 decimal places or a   % to 2 decimal places

     

   

2.16

 

3

 

2

Find the area ( probability ) to the right   of a z score of -1.90

Round to 4 decimal places or a   % to 2 decimal places - figure not drawn   to scale

 

3

 

3

Find the area ( probability ) in a right tail where the z score is 1.59

Round to 4 decimal places or a   % to 2 decimal places - draw your own figure if necessary

 

4

Find the area of the shaded region between   the z scores

Round to 4 decimal places

 

-2.32 1.09

 

5

If the area of the shaded region is 31.05% or .3105, find the z score at the question mark.

Round to 2 decimal places 

 

3

 

6

Find the z score if the NON-shaded region   indicated by the arrow is .0293

Round to 4 decimal places

 

3

 

7

When a bell curve is shaded from a 

z score of ZERO (0) all the way to positive infinity, what is the area (probability)   covered ?

3

 

8

Find the z score if the area of the shaded   region is .7172

Round to 2 decimal places

 

3

 

9

Find the z score if the area of the shaded   region is .0298

Round to 2 decimal places

 

3

 

 

PART 3

 

10.

NOTE: THE ANSWER IS NOT A ZSCORE—IT IS A %

 THIS IS A BELL CURVE PROBLEM

  

   

This is a typical bag of broken pretzels—the       pretzels are purposely broken to provide a surface for various flavor       coatings. It is found that the       average number of pieces (after whole pretzels are broken) is 301.68 pieces with a stdev of 32.8 pieces. If a random bag is selected, find the       probability that the bag will contain less than 265 broken pieces.

      

ROUND       TO 2 DECIMAL PLACES

5

 

11.

The answer is a value—not a   probability.

 

  

   

The       garbage service truck is known to wake us early in the morning. This company’s truck is almost always       on time---the average difference in their times is 13.26 minutes with a       stdev = 8.22 minutes. The company       requires the crews to be 97.22% efficient—meaning that any time below the       97.22% cutoff will result in a warning for driver and crew. Find the lowest value that will not       result in a warning—I am looking for the cutoff score. Round to 2 decimal places.

THIS IS       A BELL CURVE CUTOFF SCORE PROBLEM

5

 

12.

 

  

   

This is a tank less water heater; it has advantages and some       disadvantages. Theoretically,       a tankless water heater will provide your home with a limitless supply of       hot water with next to no warmup time. For this problem, the       average tankless takes 7.24 minutes to heat water with a stdev = 1.03       minutes ( depending on several factors). Find the probability that a       randomly selected tankless will take BETWEEN 5.98 minutes and 8.09       minutes to heat up. 

Leave answer at 2 decimal places.

5

 

13.

 

Your parents and/or   grandparents may have told you about their old television set ( “we only had 3 channels and the set had to warm-up”). It has been researched and reported that   these old tvs took an average of 15.6 seconds to warm up with a stdev= 6.08 seconds. If a sample of  16 old tvs is selected at random, find the   probability that it will take MORE than 13.07 seconds to warm up. Answer to 2 decimal places

And we didn’t have   remotes either !

5

CHAOTER 7 PROBLEMS  

  

SHARKS

5 POINTS

 

 

  

DOLLS

5 POINTS

Bonus problem: Not covered by the instructor

  

#

Problem 

Notes 

POINT VALUE

YOUR ANSWER(S)

 

Bonus 

The average size of a rhododendron   tree is 19.4 feet; if 20.5% of all   rhododendrons are higher than 22.79 feet, find the stdev. Round answer to 2   decimal places.