Question

Let X be a normal random variable with its mean equal to 40 and standard deviation equal to 5.find the following probablilties for this normal distribution
a)P(x>55) B)P(x<49)

Answer 1

find the z scores

Answer 2

i did N i got 3

Answer 3

in my data booklet there is no z score at the value of three

Answer 4

3?

Answer 5

yes

Answer 6

each z score is one standard deviation from the mean

Answer 7

i don't get you...how?

Answer 8

\[z=\frac{X-\mu}{\sigma}=\frac{55-40}{5}=3\]

Answer 9

but then @kropot72 in a data booklet there is not a score with the value of 3

Answer 10

Use the empirical rule: About 99.73% of the area of the normal distribution is included within a distance of plus and minus 3 standard deviations from the mean.

Answer 11

i've never heard of that formula before..pls show me what you mean.

Answer 12

@jazrio
you must have a weird table if you don't have a value of 3 in your table

Answer 13

a lot of the tables go up to 3.49

Answer 14

but @Zarkon my teacher gave me the table and she said that only this values will be given the rest you'll have to find out....ex:the negative z scores

Answer 15

my one stops at 2.9 only

Answer 16

you only have half of the normal table?

Answer 17

weird

Answer 18

kropot72 method will give you the answer then

Answer 19

but i dunno how to do it

Answer 20

can you help me pls

Answer 21

it would be weird to show you a way that your instructor had not taught.

Answer 22

yeah but @Zarkon you see my instructor gave me this question long time ago but i don't recall which method she used

Answer 23

100 - 99.73 = 0.27% of the area lies outside the plus and minus 3 standard deviations from the mean. We are interested in only the upper tail of the normal distribution curve. Therefore the value 0.27% must be halved.

Answer 24

@kropot72 sorry...i can't visualise

Answer 25

BTW I have a z table that goes up to z = 4. That table gives 0.1% for z = 3.