AnimalLover8
  • AnimalLover8
The time required to finish a test in normally distributed with a mean of 80 minutes and a standard deviation of 15 minutes. What is the probability that a student chosen at random will finish the test in more than 95 minutes?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
AnimalLover8
  • AnimalLover8
82% 2% 34% 16%
jim_thompson5910
  • jim_thompson5910
Do you have a TI calculator?
AnimalLover8
  • AnimalLover8
No, if I did I would be able to do many more questions.

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More answers

jim_thompson5910
  • jim_thompson5910
ok we'll use a table then
jim_thompson5910
  • jim_thompson5910
first convert the raw score x = 95 to a z-score use the formula z = (x-mu)/sigma
jim_thompson5910
  • jim_thompson5910
in this case, mu = 80 and sigma = 15
AnimalLover8
  • AnimalLover8
What is the "raw score"?
jim_thompson5910
  • jim_thompson5910
x = 95 is the raw score
jim_thompson5910
  • jim_thompson5910
it's the score on the test the z-score is the transformed score to the standard normal distribution
jim_thompson5910
  • jim_thompson5910
z = (x-mu)/sigma z = (95-80)/15 z = ???
AnimalLover8
  • AnimalLover8
So z=...1?
jim_thompson5910
  • jim_thompson5910
yes z = 1
jim_thompson5910
  • jim_thompson5910
ie, z = 1.00
jim_thompson5910
  • jim_thompson5910
Now use a table like this one https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf locate the row that starts with `1.0` and find the column that has `.00` at the top the intersection of this row and column has the number ______ (fill in the blank)
AnimalLover8
  • AnimalLover8
.84134
AnimalLover8
  • AnimalLover8
I don't understand what this number actually is.
jim_thompson5910
  • jim_thompson5910
this number represents the probability of getting a z-score less than 1.00 in notation form, we say `P(Z < 1.00) = 0.84134` so there's approx a 84.134 % of getting a z-score less than 1.00 in other words, there is a 84.134 % chance of getting a test score less than 95
jim_thompson5910
  • jim_thompson5910
subtract 0.84134 from 1 to get the probability of getting a score larger than z = 1 or x = 95
AnimalLover8
  • AnimalLover8
0.269... ?
jim_thompson5910
  • jim_thompson5910
compute 1 - 0.84134
AnimalLover8
  • AnimalLover8
Wait so how do you get the probability from there?
jim_thompson5910
  • jim_thompson5910
1 - 0.84134 = 0.15866
jim_thompson5910
  • jim_thompson5910
0.15866 = 15.866% which rounds to 16%
jim_thompson5910
  • jim_thompson5910
we have some normal curve |dw:1440808310147:dw|
AnimalLover8
  • AnimalLover8
OOOOOOH!
jim_thompson5910
  • jim_thompson5910
|dw:1440808329487:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1440808367344:dw|
AnimalLover8
  • AnimalLover8
Yeah. :) Thank you so much!
jim_thompson5910
  • jim_thompson5910
I'm glad that everything is making sense now
AnimalLover8
  • AnimalLover8
Me too, I usually pick things up very quickly, but I just couldn't hack this question. :)

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