The random variable Y is normally distributed with a mean of 470, and the value Y= 340 is at the 15th percentile of the distribution. Of the following, which is the best estimate of the standard deviation of the distribution? A. 125 B. 135 C. 145 D. 155 E. 165

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The random variable Y is normally distributed with a mean of 470, and the value Y= 340 is at the 15th percentile of the distribution. Of the following, which is the best estimate of the standard deviation of the distribution? A. 125 B. 135 C. 145 D. 155 E. 165

Mathematics
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  • phi
yes, and the 15th percentile is at about -1 std dev
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I'm so sorry i have to brb my mom needs help upstairs brb
  • phi
-1 std deviation means you are one standard deviation less than the mean the mean is 470 and 15th percentile is 340 the difference is about 1 standard deviation
  • phi
based on the choices, we have to be more accurate. based on your curve, -1 std deviation is at the 16th percentile (2+14= 16) and we are given the 15th percentile = 340 |dw:1436991677454:dw|
  • phi
the red line at -1 std dev is a little bit closer to the mean... so the difference should be a little bit less than 130
Hey so how did you know that it was at the 16th percentile?
oh wait nvm i see it now
so if it's a little bit less than 130 it's 125?
  • phi
if you have a z-table, you could look up the z score for 0.15 (I think it's about 1.04) and then say 1.04*s= 130 s= 130/1.04 s= 125
hmmm ok i got it thank you !!

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