Question

Okay, so I am currently learning about normal distribution, and I don't know how to do the question that looks like this (I'll try my best to convey it, but I don't have all the right symbols on my laptop): P(X is less than or equal to 64)
The mean is 76 and the standard deviation is 6.
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- Please no vague or unsure answers.

Answer 1

x = 64 is the given raw score

the first step is to convert this to a standard z-score


z = (x - mu)/sigma
z = (x - 76)/6
z = (64 - 76)/6
z = -12/6
z = -2


so the raw score of x = 64 corresponds to the standard z-score of z = -2

z = -2 means that the raw score x = 64 is 2 standard deviations below the mean (mu = 76)

Answer 2

now use a table to compute P(z < -2)

a table like this is usually found in the back of your stats book

http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

Answer 3

THANK YOU SO VERY MUCH!

Answer 4

you're welcome

Answer 5

you can also use the `normalcdf` function found on TI83, TI84, etc calculators

http://tibasicdev.wikidot.com/normalcdf

but your teacher will probably want you to use the table instead

Answer 6

How about if you are finding p(x is GREATER THAN or equal to 70)
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-same mean and standard deviation :)

Answer 7

Rule:

P(x > k) = 1 - P(x < k)

where k is some fixed number

Answer 8

using the rule, we know that

P(x > 70) = 1 - P(x < 70)

Answer 9

so you need to follow the steps to compute P(x < 70) first

then subtract that result from 1

Answer 10

oh and it doesn't matter if you have `greater than` or `greater than or equal to` since the two lead to the same answer

Answer 11

Okay last question: what if it has

p(x is greater than or equal to 85 but less than or equal to 91.
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-I got .93 and .43 as the "Z's" for both of them, then I tried to subtract them from each other: .93-.43, but I think I did it wrong. (Sorry if that doesn't make any sense and also thank you so much for your help).

Answer 12

Rule

\[\Large P\left(a < x < b\right) = P(x < b) - P(x < a)\]

in this case, `b > a`

Answer 13

\[\Large P\left(85 \le x \le 91\right) = P(x \le 91) - P(x \le 85)\]

Answer 14

Step 1) Compute \(\Large P(x \le 91)\). Call this result M

Step 2) Compute \(\Large P(x \le 85)\). Call this result N

Step 3) Compute `M - N`