Normal Distribution Worksheet 7 - Mr. K's Virtual World of ...



Normal Distribution Worksheet 7.4

Name_________________________ Period _______

1. A machine is used to put nails into boxes. It does so such that the actual number of nails in a box is normally distributed with a mean of 106 and a standard deviation of 2.

A. What percentage of boxes contains:

a) more than 104 nails? ___________

b) more than 110 nails? ___________

c) less than 102 nails? ___________

d) between 102 and 112 nails? ___________

e) between 100 and 106 nails? ___________

B) What is the z-score for a box that contains:

a) 101 nails? ___________

b) 107 nails? ___________

c) 111 nails? ___________

d) 99 nails? ___________

C) What is the percentile for a box that contains;

a) 101 nails? ___________

b) 107 nails? ___________

c) 111 nails? ___________

d) 99 nails? ___________

2. The heights of the people on the planet Ixx are normally distributed with a mean of 40 inches and a standard deviation of 5inches. (They are a vertically diverse group of people.)

A. What percentage of the Ixxians are:

a) over 30 inches? ________

b) over 45 inches? ________

c) under 50 inches? ________

d) under 40 inches? ________

e) between 35 and 55 inches tall? ________

f) between 25 and 35 inches tall? ________

B) What is the z-score for an Ixxian that is:

a) 32 inches tall? ________

b) 47 inches tall? ________

c) 51 inches tall? ________

C) What is the percentile for an Ixxian that is:

a) 32 inches tall? ________

b) 47 inches tall? ________

c) 51 inches tall? ________

Bonus: You must show your work !!!!!

What is the HEIGHT of an Ixxian who is at the 60th percentile?

_________

You may use the following charts to help you solve the problems but you will need to fill in the blanks for the first chart in order to do so.

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