Question

Outcome A is 1 standard deviation below the mean. Outcome B is 2 standard deviations above the mean. Which outcome is more likely?



It is impossible to tell

Outcome A is more likely

They are both equally likely

Outcome B is more likely.

Answer 1

is it a normal distribution?

Answer 2

Yes

Answer 3

then we should recollect that the mean defines what is normally expected. the farther we are from what is expected, the less likely it is to occur.

Answer 4

So it would be outcome A is more likely?

Answer 5

that is how i read it yes. A is closer to normality than B, therefore it is more likely

Answer 6

Could you help me with another problem?

Answer 7

depends on the problem :)

Answer 8

A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 65 mph and a standard deviation of 8 mph. What is the probability that a car picked at random is travelling at 71 mph?



0.034

0.040

0.061

0.028

Answer 9

what do you know of a zscore calculation ? your material might call it a standard score

Answer 10

a standard normal distribution has a mean of 0, so we subtract the mean from all data points since mean - mean = 0

a standard normal distribution has a standard deviation of 1, so we divide our results by the samples standard deviation since anything divided by itself is 1

this gives us the formula:\[z=\frac{x-mean }{sd}\]
we use this zscore to look up a table to find the probability with, or we simply use a stats calculator like a ti83 and it does it for us

Answer 11

71-65 = 6

6/8 = .75

so 71 is .75 standard deviations from the mean of 65

if we are looking in a left tail table, we would want to find where the row: 0.7 crosses with the column .05

Answer 12

but if got some concern with the question, its asking for a car traveling at a specific speed, and not for say 71 and less, or 71 and greater.

probabilities are an area under the curve and we would need a range to play with, not an exact point.

Answer 13

Ok i sorta understand, its so many steps i get so confused...

Answer 14

Would ther answer be C?

Answer 15

i cant determine if its C or not.

The probability that a car is traveling at 71 or less is: .7734
The probability that a car is traveling at 71 or more is: .2266

but i cant determine what the probability is that a car is traveling exactly at 71. Ive either forgotten it, or never learned it to start with.

Answer 16

the only thought i have coming to me is to address it as a binomial approximation

Answer 17

Yea true, thanks for helping me this much though!!

Answer 18

good luck

Answer 19

Do you know this?
The shape of the graph of a normal distribution is:



Unpredictable

Not symmetrical

Symmetrical

Flat

Answer 20

i do, what are your thoughts?

Answer 21

C

Answer 22

the curve looks the same on the left as it does on the right, so yes, it is symmetrical

Answer 23

The probability of each outcome in a normal distribution is the same.



True

False
this would be false right?
Sorry i just want to make sure so i know when it comes too my big test!

Answer 24

id pick false as well yes