Question

Check my answers? normal distribution and advanced algebra

Answer 1

The number of nails of a given length is normally distributed with a mean length of 5 in. and a standard deviation of 0.03 in. In a bag containing 120 nails, how many nails are between 4.97 in. long and 5.03 in. long?

about 41 nails
about 60 nails
about 82 nails
about 57 nails

Answer 2

@dumbcow

Answer 3

i got D

Answer 4

If \(X\) is the length of the snails, it is normally distributed. What you can do is find the percentage (or probability) of the snail lengths being between 4.97 and 5.03 in long as:
\(P(\le 4.97 \le X \le 5.03)\)

Then you can standardize X and use a normal distribution table to find this percentage, and then multiply that result by 120 to find the # of snails.

Answer 5

wait what lol you lost me at standardize

Answer 6

i have to draw the bell curve right?

Answer 7

Did you see this:
\(Z = \dfrac{X-\mu}{\sigma}\)

Answer 8

OHHHHH

Answer 9

lol

Answer 10

that formula is used to say what we call "standardizing the normal distribution" :)

Answer 11

http://www.blackjackapprenticeship.com/wp-content/uploads/2012/05/bell-curve-3.001.png

Answer 12

did i get that right?

Answer 13

ohh

Answer 14

give me one sec

Answer 15

yes and
\[\frac{4.97 - 5}{.03} = -1\]

use the image i posted to find probability of being within -1 std dev and 1 std dev from mean

Answer 16

wait s what do i do with the 1 and -1?

Answer 17

i know i have to do something with 120 but i dont remember

Answer 18

did you see the normal curve i posted?

Answer 19

yes its 34.1

Answer 20

so i have to add that twice to find the difference from 1 to -1

Answer 21

correct

Answer 22

68.2

Answer 23

thats the probability of being in that range

now the 120 is the total number which represents the entire bell curve or 100%
68.2% of 120 will give you the number of nails within the range of -1 to 1